CBSE Class 9 Science Gravitation Worksheet Set B

 

 

Question. SI unit of G is
(a) \( N^2–m^2/kg \)
(b) \( N–m^2/kg \)
(c) \( N–m/kg \)
(d) \( N -m^2/kg^2 \)
Answer: D

Question. Choose the correct statement of the following:
(a) All bodies repel each other in this universe.
(b) Our earth does not behave like a magnet.
(c) Acceleration due to gravity is \( 8.9 \text{ m/s}^2 \).
(d) All bodies fall at the same rate in vacuum.
Answer: D

Question. Maximum weight of a body is
(a) at the centre of the earth
(b) inside the earth
(c) on the surface of the earth
(d) above the surface of earth
Answer: C

Question. If the distance between two masses be doubled, then the force between them will become
(a) \( 1/4 \) times
(b) \( 4 \) times
(c) \( 1/2 \) times
(d) \( 2 \) times
Answer: A

Question. A body falls freely towards the earth with
(a) uniform speed
(b) uniform velocity
(c) uniform acceleration
(d) none of these
Answer: C

Question. If the mass of a body is M on the surface of the earth, then its mass on the surface of the moon will be
(a) \( M/6 \)
(b) \( M \)
(c) \( M + 6 \)
(d) zero
Answer: B

Question. Weight
(a) is a vector quantity
(b) of a body in interplanetary space is maximum
(c) increases when the bodies go up
(d) none of these
Answer: A

Question. The value of g near the earth’s surface is
(a) \( 8.9 \text{ m/s}^2 \)
(b) \( 8.9 \text{ m/s} \)
(c) \( 9.8 \text{ m/s}^2 \)
(d) \( 9.8 \text{ m/s} \)
Answer: C

Question. A geostationary satellite
(a) moves faster than the near earth satellite
(b) has a time period less that of a near earth satellite
(c) revolves about the polar axis
(d) is stationary in space
Answer: C

Question. The force of gravitation between two bodies depend upon
(a) their separation
(b) gravitational constant
(c) product of their masses
(d) all of these
Answer: D

Question. When an object is thrown up, the force of gravity
(a) acts in the direction of the motion
(b) acts in the opposite direction of the motion
(c) remains constant as the body moves up
(d) increases as the body moves up
Answer: B

Question. The force of gravitation exists
(a) everywhere in the universe
(b) at the surface of the earth only
(c) inside the earth only
(d) at the surface of the moon only
Answer: A

Question. \( 1 \text{ kg wt} \) is equal to
(a) \( 9.8 \text{ N} \)
(b) \( 980 \text{ N} \)
(c) \( 98 \text{ N} \)
(d) none of these
Answer: A

Question. \( 1 \text{ kg wt} \) is equal to
(a) \( 980 \text{ dynes} \)
(b) \( 9.80 \text{ dynes} \)
(c) \( 98 \text{ dynes} \)
(d) none of these
Answer: A

Question. The value of G does not depend on
(a) nature of the interacting bodies
(b) size of the interacting bodies
(c) mass of the interacting bodies
(d) all of these
Answer: D

 

EXERCISE - II (COMPETITIVE CORNER)

 

Question. If the distance between two masses be doubled, then the force between them will become
(a) \( 1/4 \) times
(b) \( 4 \) times
(c) \( 1/2 \) times
(d) \( 2 \) times
Answer: A

Question. How does the force of gravitation between two objects change when the distance between them is reduced to half?
(a) increases 4 times
(b) increases 2 times
(c) increases 16 times
(d) increases 32 times
Answer: D

Question. What happens to the gravitational force between two objects, if the mass of one object is doubled?
(a) increases 4 times
(b) increases 2 times
(c) increases 16 times
(d) increases 32 times
Answer: B

Question. What happens to the gravitational force between two objects, if the distance between the objects is tripled?
(a) becomes \( 1/9 \) times
(b) becomes \( 1/3 \) times
(c) becomes \( 1/27 \) times
(d) becomes 9 times
Answer: A

Question. What happens to the gravitational force between two objects, If the masses of both the objects are doubled?
(a) becomes 2 times
(b) becomes 8 times
(c) becomes \( 1/4 \) times
(d) becomes 4 times
Answer: D

Question. Calculate the gravitational force of attraction between a woman weighing 50 kg and her child of 12 kg separated by a distance of 2 m.
(a) \( 1.0 \times 10^{-10} \text{ N} \)
(b) \( 1.0 \times 10^{-11} \text{ N } 10^2 \)
(c) \( 1.0 \times 10^{-9} \text{ N} \)
(d) \( 1.0 \times 10^{-8} \text{ N} \)
Answer: D

Question. The gravitational force of attraction between two bodies is \( F_1 \). If the mass of each body is doubled and the distance between them is halved, then the gravitational force between them is \( F_2 \). Then
(a) \( F_1 = F_2 \)
(b) \( F_2 = 4F_1 \)
(c) \( F_2 = 8F_1 \)
(d) \( F_2 = 16F_1 \)
Answer: D

Question. Find the gravitational force between a body of 1 kg and the earth (mass of earth \( = 6 \times 10^{24} \text{ kg} \)). The radius of earth is \( 6.4 \times 10^6 \text{ m} \).
(a) \( 19.6 \text{ N} \)
(b) \( 9.8 \text{ N} \)
(c) \( 20 \text{ N} \)
(d) \( 36.08 \text{ N} \)
Answer: B

Question. Which of the following is correct:
(a) Moon has no atmosphere
(b) The tangential acceleration of a planet is zero
(c) Gravitational force is a medium dependent force
(d) Gravitational force is a conservative force
Answer: C

Question. The SI unit of g is
(a) \( \text{m}^2/\text{s} \)
(b) \( \text{m/s}^2 \)
(c) \( \text{s/m}^2 \)
(d) \( \text{m/s} \)
Answer: B

Question. The value of acceleration due to gravity near the earth’s surface is
(a) \( 8.9 \text{ m/s}^2 \)
(b) \( 8.9 \text{ m/s} \)
(c) \( 9.8 \text{ m/s}^2 \)
(d) \( 9.8 \text{ m/s} \)
Answer: C

Question. The relation between ‘g’ and ‘G’ is
(a) \( g = \frac{GM}{R^2} \)
(b) \( \frac{GR^2}{M} \)
(c) \( g = GMR^2 \)
(d) \( \frac{G}{MR^2} \)
Answer: A

Question. All bodies whether large or small fall with the
(a) Same force
(b) Same acceleration
(c) Same velocity
(d) Same momentum.
Answer: B

Question. In vaccum all freely falling objects
(a) Have the same speed
(b) Have the same velocity
(c) Have the same acceleration
(d) Have the same force.
Answer: C

Question. The ratio of \( g_{\text{moon}} \) to \( g_{\text{earth}} \) is
(a) \( 6 \)
(b) \( 1/6 \)
(c) \( 4 \)
(d) \( 1/4 \)
Answer: B

Question. The unit of the quantity g/G in SI will be
(a) \( \text{Kgm}^{–2} \)
(b) \( \text{mKg}^{–2} \)
(c) \( \text{m}^2\text{Kg}^{–1} \)
(d) \( \text{Kg}^2\text{m}^{–1} \)
Answer: A

Question. The ratio of SI units to CGS units of g is
(a) \( 10^2 \)
(b) \( 10 \)
(c) \( 10^{-1} \)
(d) \( 10^{-2} \)
Answer: A

Question. The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man can jump to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B?
(a) \( 2/9 \text{ m} \)
(b) \( 18 \text{ m} \)
(c) \( 6 \text{ m} \)
(d) \( 2/3 \text{ m} \).
Answer: B

Question. The value of ‘g’ at poles is
(a) Greater than the value at the equator
(b) Less than the value at the equator
(c) Equal to the value at the equator
(d) None of these
Answer: A

Question. Two spheres of masses m and M are situated in air and the gravitational fore between them is F. The space around the masses is now filled with liquid of specific gravity 3. The gravitational force will now be
(a) \( 3F \)
(b) \( F \)
(c) \( F/3 \)
(d) \( F/9 \).
Answer: B

Question. The value of acceleration due to gravity on the surface of earth be denoted by g. If the radius of earth is 6400km, then what will be the acceleration due to gravity at a point 3200km above the surface of earth?
(a) \( g/9 \)
(b) \( 2g/9 \)
(c) \( 4g/9 \)
(d) \( g/2 \).
Answer: C

Question. The value of g on the earths surface is \( 980 \text{ cm/s}^2 \). Its value at a height of 64km from the earths surface is
(a) \( 960.40 \text{ cm/s}^2 \)
(b) \( 984.90 \text{ cm/s}^2 \)
(c) \( 982.45 \text{ cm/s}^2 \)
(d) \( 977.55 \text{ cm/s}^2 \)
Answer: A

Question. At what height above the earths surface does the acceleration due to gravity fall to 1% of its value at the earths surface?
(a) \( R \)
(b) \( 5R \)
(c) \( 10R \)
(d) \( 9R \).
Answer: D

Question. The value of g is with depth
(a) Increases
(b) Decreases
(c) Does not change
(d) increases or decreases
Answer: B

Question. A body is raised to a height h so that the force of gravity on the body is 1% of the value on the surface of Earth. If the radius of the Earth is 6400km, then the value of h is
(a) \( 57600 \text{ km} \)
(b) \( 5999 \text{ km} \)
(c) \( 9.8 \text{ km} \)
(d) \( 0.98 \text{ km} \)
Answer: A

Question. A man weights W on the surface of Earth. What is the weight at a height equal to R?
(a) \( W \)
(b) \( W/2 \)
(c) \( W/4 \)
(d) \( W/8 \)
Answer: C

Question. Radius of Earth is 6000km. Weight of a body on the surface of Earth is 120kg wt. If it is taken to a height of 2000km above the surface of Earth, its weight is
(a) \( 60 \text{ kg.wt} \)
(b) \( 40 \text{ kg.wt} \)
(c) \( 67.5 \text{ kg.wt} \)
(d) \( 47.5 \text{ kg.wt} \)
Answer: C

Question. The acceleration due to gravity is reduced to a value one-fourth of that on the surface of Earth at a height h where h is equal to \( xR_e \) (radius of Earth). The value of x is
(a) \( 1 \)
(b) \( 1/2 \)
(c) \( 1/3 \)
(d) \( 1/4 \)
Answer: A

Question. The value of ‘g’ at a certain height h above the free surface of Earth is \( x/4 \) where x is the value of ‘g’ at the surface of Earth. The height h is
(a) \( R \)
(b) \( 2R \)
(c) \( 3R \)
(d) \( 4R \)
Answer: A

Question. A body weights 63N on the surface of the Earth. At a height h above the surface of Earth, its weight is 28N while at a depth h below the surface of Earth, the weight is 31.5N. The value of h is
(a) \( 0.4R \)
(b) \( 0.5R \)
(c) \( 0.8R \)
(d) \( R \)
Answer: B

Question. The gravitational field due to a mass distribution is \( I = K/r^3 \) in the X-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is
(a) \( K/x \)
(b) \( K/2x \)
(c) \( K/x^2 \)
(d) \( K/2x^2 \).
Answer: D

Question. The rotation period of earth satellite close to the surface of earth is 83 minutes. The time period of another earth satellite in an orbit at a distance of three earth radius from its surface will be
(a) 83 minutes
(b) \( 83 \times \sqrt{8} \) minutes
(c) 249 minutes
(d) 664 minutes.
Answer: D

Question. A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1%, its speed will
(a) increase by 1%
(b) increase by 0.5%
(c) decrease by 1%
(d) decrease by 0.5%.
Answer: B

 

ADDITIONAL MCQs

 

Question. If g is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass m raised from the surface of earth to a height equal to the radius R of the earth is
(a) \( \frac{1}{2}mgR \)
(b) \( 2mgR \)
(c) \( mgR \)
(d) \( 1/4 \text{ mgR} \).
Answer: A

Question. The period of revolution of a certain planet in an orbit of radius R is T. Its period of revolution in an orbit of radius 4R will be
(a) \( 2T \)
(b) \( 2\sqrt{2}T \)
(c) \( 4T \)
(d) \( 8T \).
Answer: D

Question. If the radius of earth were to decrease by 1%, its mass remaining the same, the acceleration due to gravity on the surface of earth will
(a) increase by 1%
(b) increase by 2%
(c) decrease by 1%
(d) increase by 2%.
Answer: B

Question. According to Kepler’s laws, which of the following is correct?
(a) \( T \propto R^{3/2} \)
(b) \( T \propto R^3 \)
(c) \( T \propto R^{2/3} \)
(d) \( T \propto R^2 \).
Answer: A

Question. A space craft is launched in a circular orbit very close to Earth. What additional velocity should be given to the space craft so that it might escape the Earth’s gravitational pull? (Radius of the Earth \( = 6400 \text{ km} \); \( g = 9.8 \text{ m/s}^2 \))
(a) \( 11.2 \text{ km/s} \)
(b) \( 3.25 \text{ km/s} \)
(c) \( 85 \text{ km/s} \)
(d) \( 20.2 \text{ km/s} \).
Answer: B

Question. A body of mass m is placed on earth surface which is taken from earth surface to a height of h = 3R, then change in gravitational potential energy is
(a) \( \frac{1}{4}mgR \)
(b) \( \frac{2}{3}mgR \)
(c) \( \frac{3}{4}mgR \)
(d) \( \frac{1}{2}mgR \).
Answer: C

Question. A string has a tension T when it is holding a solid block below the surface of a liquid (liquid having density greater than that of solid) and the system is at rest. The tension in the string when the system has an acceleration a in upward direction is
(a) \( T(1+g/a) \)
(b) \( T(1-g/a) \)
(c) \( T(1+a/g) \)
(d) \( T(1-a/g) \).
Answer: C

Question. A wooden block with a coin placed on it’s top, floats in water as in the figure. The distance \( \ell \) and h are also shown there. After some time, the coin falls into the water, then
(a) \( \ell \) increases and h decreases
(b) \( \ell \) decreases and h increases
(c) both decrease
(d) both increases.
Answer: C

Question. An icecube has a stone frozen inside it. The cube floats in a beaker filled with water when the ice melts, then
(a) there is no change in level of water
(b) the water level decreases
(c) the water level increases
(d) the water level first increases then decreases.
Answer: B

Question. A piece of ice is floating in a jar containing water. When the ice melts, then the level of water.
(a) rises
(b) falls
(c) remains unchanged
(d) rises or falls depending upon the mass of ice
Answer: C

Question. Find the density of a block of wood that floats in water with 0.1 of its volume above water
(a) \( 0.9 \text{ g/cc} \)
(b) \( 0.9 \)
(c) \( 0.1 \text{ g/cc} \)
(d) \( 0.1 \)
Answer: A

Question. A body of volume 100 cc floats immersed completely in water contained in a jar. The mass of water and jar before immersion of the body was 700 g. After immersion mass of water and jar will be
(a) 500 g
(b) 700 g
(c) 100 g
(d) 800 g
Answer: D

Question. Two bodies of equal mass with volumes V and 2V are equalized on a balance. The large body is then immersed in oil of density \( \rho = 0.9 \text{ g/cc} \). What must be the density of the liquid in which the smaller body is simultaneously immersed so as not to disturb the equilibrium of the balance ?
(a) \( 0.9 \text{ g/cc} \)
(b) \( 1.8 \text{ g/cc} \)
(c) \( 0.45 \text{ g/cc} \)
(d) \( 1.35 \text{ g/cc} \)
Answer: B

Question. An empty balloon weighs \( W_1 \). If air equal in weight to W is pumped into the balloon, the weight of the balloon becomes \( W_2 \). Suppose that the density of air inside and outside the balloon is same then
(a) \( W_2 = W_1 + W \)
(b) \( W_2 = \sqrt{W_1W} \)
(c) \( W_2 = W_1 \)
(d) \( W_2 = W_1 – W \)
Answer: C

Question. A body of mass 120 kg and density \( 600 \text{ kg/m}^3 \) floats in water. What additional mass could be added to the body so that the body will just sink?
(a) 20 kg
(b) 80 kg
(c) 100 kg
(d) 120 kg
Answer: B

Question. By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg (density \( = 13.6 \text{ g/cm}^3 \)). Using the straw, he can drink water from a glass upto a maximum depth of
(a) 10 cm
(b) 75 cm
(c) 13.6 cm
(d) 1.36 cm
Answer: C

 

EXERCISE - III (CBSE CORNER)

 

VERY SHORT ANSWER TYPE QUESTIONS

Question. Who gave the Universal law of gravitation
Answer: Issac Newton gave the universal law of gravitation.

Question. What do you mean by gravitation ?
Answer: The force of attraction between any two particles in the universe is called gravitation.

Question. State Universal law of gravitation.
Answer: The force of attraction between two particles or objects is (i) directly proportional to the product of the masses of the objects and (ii) inversly proportional to the square of the distance between them.

Question. Write an expression for the gravitational force between the earth and a body on the earth.
Answer: \( F = \frac{GMm}{r^2} \), where M is the mass of the earth, m is the mass of the body, r is the radius of the earth and G is the universal gravitational constant.

Question. The distance between two particles is decreased. Will the gravitational force between them increase or decrease?
Answer: \( F \propto 1/r^2 \). So, gravitational force (F) increases when the distance (r) decreases.

Question. An iron ball exerts a force F on the rubber ball. How much force, the, rubber ball will exert on the iron ball ?
Answer: The rubber ball also exerts the same force F on the iron ball.

Question. Define Universal gravitational constant (G)..
Answer: Universal gravitational constant is defined as the force of attraction between two objects of unit masses separated by unit distance.

Question. Write down the unit of ‘G’ in S.I.
Answer: \( \text{Nm}^2/\text{kg}^2 \).

Question. What is the value of ‘G’ ?
Answer: \( G = 6.673 \times 10^{-11} \text{ Nm}^2/\text{Kg}^2 \).

Question. The value of \( G = 6.673 \times 10^{-11} \text{ Nm}^2 \text{ kg}^{–2} \) on the surface of the earth. What is the value of G on the surface of the moon ?
Answer: The value of G on the surface of the moon = value of G on the surface of the earth (i.e., \( 6.673 \times 10^{–11} \text{ Nm}^2 \text{ kg}^{–2} \))

Question. The gravitational force between the earth and an object is known as ............
Answer: Gravity or force of gravity.

Question. The gravitational force between two objects on the earth is 2 N. What will be the gravitational force between these two objects on the surface of the moon ?
Answer: Same force i.e. 2 N.

Question. Tides in oceans are formed due to gravitational force between ...........and.............
Answer: the moon, the earth.

Question. Name the force which is responsible for the revolution of planets around the sun.
Answer: Gravitational force of attraction between the planet and the sun. This force provides the necessary centripetal force to the planet to move in a circular orbit around the sun.

Question. Name the force which is responsible for the revolution of moon around the earth.
Answer: The Gravitational force between the earth and the moon provides the centripetal force to the moon to move in a circular path around the earth.

Question. How does the gravitational force between two bodies varies with r ?
Answer: \( F \propto 1/r^2 \).

Question. Is acceleration due to gravity on the surface of moon less or more than the acceleration due to gravity on the surface of earth ?
Answer: Acceleration due to gravity on the surface of the moon is less than that on the surface of the earth.

Question. Write the expression for the acceleration due to gravity. \( g = \frac{GM}{R^2} \)
Answer: \( g = \frac{GM}{R^2} \)

Question. What is the SI unit of acceleration due to gravity (g)
Answer: \( \text{ms}^{–2} \)

Question. What is the value of acceleration due to gravity on the surface of earth ?
Answer: \( g = 9.8 \text{ ms}^{–2} \)

Question. Is acceleration due to gravity a scalar or a vector quantity ?
Answer: It is a vector quantity.

Question. What is the value of acceleration due to gravity on the surface of moon ?
Answer: \( g = 1.6 \text{ ms}^{–2} \) on the surface of moon.

Question. Acceleration due to gravity on the surface of moon = ........ × Acceleration due to gravity on the surface of the earth.
Answer: \( 1/6 \)

Question. Where is the acceleration due to gravity more : at poles or at equator ?
Answer: At poles

Question. What is the value of ‘g’ at the centre of the earth ?
Answer: Zero.

Question. What will be the direction of acceleration due to gravity if the body is thrown vertically upward?
Answer: The direction of acceleration due to gravity is always towards the centre of the earth i.e. in the downward direction.

Question. Define mass of a body.
Answer: Mass of a body is defined as the quantity of matter contained in the body.

Question. Why is mass known as inertial mass ?
Answer: Since mass is a measure of the inertia of a body, so the mass is known as inertial mass.

Question. What is the SI unit of mass ?
Answer: S.I. unit of mass is kilogram

Question. Is mass of a body a scalar or a vector physical quantity.
Answer: Mass is a scalar physical quantity.

Question. The mass of a body at the equator is 20 kg. What will be the mass of this body at the poles?
Answer: 20 kg.

Question. Define weight of a body.
Answer: The force with which a body is attracted by the earth is known as the weight of the body.

Question. Write a relation between the mass and weight of the body.
Answer: \( W = mg \)

 

NUMERICAL PROBLEMS

 

Question. What is the gravitational acceleration of a spaceship at a distance equal to two Earth’s radius from the centre of the Earth?
Answer: \( 2.45 \text{ m/s}^2 \)

Question. A boy on a cliff 49 m high drops a stone. One second later, he throws a second stone after the ftrst. They both hit the ground at the same time. With what speed did he throw the second stone ?
Answer: \( 12.1 \text{ m/s} \)

Question. A stone drops from the edge of the roof. It passes a window 2 m high in 0·1 s. How far is the roof above the top of the window?
Answer: \( 19.4 \text{ m} \)

Question. A particle is dropped from a tower 180 m high. How long does it take to reach the ground? What is the velocity when it touches the ground? Take \( g = 10 \text{ m/s}^2 \).
Answer: \( 6 \text{ s, } 60 \text{ m/s} \)

Question. To estimate the height of a bridge over a river, a stone is dropped freely on the river from the bridge. The stone takes 2 s to touch the water surface in the river. Calculate the height of the bridge from the water level. Take \( g = 9.8 \text{ m/s}^2 \).
Answer: \( 19.6 \text{ m} \)

Question. How much would a 70 kg man weigh on moon? What will be his mass on Earth and Moon? Given g on Moon \( = 1.7 \text{ m/s}^2 \).
Answer: \( 119 \text{ N, } 70 \text{ kg, } 70 \text{ kg} \)

Question. A body has a weight of 10 kg on the surface of Earth. What will be its mass and weight when taken to the centre of Earth ?
Answer: \( 10 \text{ kg, Zero} \)

Question. A force of 2 kg wt acts on a body of mass 4·9 kg. Calculate its acceleration.
Answer: \( 4 \text{ m/s}^2 \)

Question. A force of 20 N acts upon a body whose weight is 9·8 N. What is the mass of the body and how much is its acceleration ?
Answer: \( 1 \text{ kg, } 20 \text{ m/s}^2 \)

Question. A man weighs 600 N on the Earth. What is its mass? Take \( g = 10 \text{ m/s}^2 \). If he were taken on Moon, his weight would be 100 N. What is his mass on Moon? What is acceleration due to gravity on Moon?
Answer: \( 60 \text{ kg, } 60 \text{ kg, } 1.67 \text{ m/s}^2 \)

Question. A car falls off a ledge and drops to the ground in 0·5 s. Let \( g = 10 \text{ m/s}^2 \) (for simplifying the calculations). (i) What is its speed on striking the ground? (ii) What is its average speed during 0·5 s? (iii) How high is the ledge from the ground?
Answer: (i) \( 5 \text{ m/s} \) (ii) \( 2.5 \text{ m/s} \) (iii) \( 1.25 \text{ m} \)

Question. An object is thrown vertically upwards and rises to a height of 10 m. Calculate (i) the velocity with which the object was thrown upwards and (ii) the time taken by the object to reach the highest point.
Answer: \( 14 \text{ m/s, } 1.43 \text{ s} \)

Question. Mass of an object is 10 kg. What is its weight on Earth?
Answer: \( 98 \text{ N} \)

Question. An object weighs 10 N when measured on the surface of the Earth. What would be its weight when measured on the surface of Moon ?
Answer: \( 1.67 \text{ N} \)

Question. Calculate the value of acceleration due to gravity on Moon. Given mass of Moon \( = 7.4 \times 10^{22} \text{ kg} \), radius of Moon \( = 1740 \text{ km} \).
Answer: \( 1.63 \text{ m/s}^2 \)

Question. Suppose a planet exists whose mass and radius both are half those of Earth. Calculate the acceleration due to gravity on the surface of this planet.
Answer: \( 19.6 \text{ m/s}^2 \)

Question. A ball is thrown up with a speed of 15 m/s. How high will it go before it begins to fall? Take \( g = 9.8 \text{ m/s}^2 \).
Answer: \( 11.48 \text{ m} \)

Question. How does the force of gravitation between two objects change when the distance between them is reduced to half?
Answer: \( 4F \)

Question. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?
Answer: The acceleration due to gravity is independent of the mass of the falling object.

Question. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is \( 6 \times 10^{24} \text{ kg} \) and radius of the earth is \( 6.4 \times 10^6 \text{ m} \).)
Answer: \( 9.8 \text{ N} \)

VERY SHORT ANSWER TYPE QUESTIONS

Question. Who gave the Universal law of gravitation
Answer: Issac Newton gave the universal law of gravitation.

Question. What do you mean by gravitation ?
Answer: The force of attraction between any two particles in the universe is called gravitation.

Question. State Universal law of gravitation.
Answer: The force of attraction between two particles or objects is (i) directly proportional to the product of the masses of the objects and (ii) inversly proportional to the square of the distance between them.

Question. Write an expression for the gravitational force between the earth and a body on the earth.
Answer: \( F = \frac{GMm}{r^2} \), where M is the mass of the earth, m is the mass of the body, r is the radius of the earth and G is the universal gravitational constant.

Question. The distance between two particles is decreased. Will the gravitational force between them increase or decrease?
Answer: \( F \propto 1/r^2 \). So, gravitational force (F) increases when the distance (r) decreases.

Question. An iron ball exerts a force F on the rubber ball. How much force, the, rubber ball will exert on the iron ball ?
Answer: The rubber ball also exerts the same force F on the iron ball.

Question. Define Universal gravitational constant (G)..
Answer: Universal gravitational constant is defined as the force of attraction between two objects of unit masses separated by unit distance.

Question. Write down the unit of ‘G’ in S.I.
Answer: \( \text{Nm}^2/\text{kg}^2 \).

Question. What is the value of ‘G’ ?
Answer: \( G = 6.673 \times 10^{-11} \text{ Nm}^2/\text{Kg}^2 \).

Question. The value of \( G = 6.673 \times 10^{-11} \text{ Nm}^2 \text{ kg}^{–2} \) on the surface of the earth. What is the value of G on the surface of the moon ?
Answer: The value of G on the surface of the moon = value of G on the surface of the earth (i.e., \( 6.673 \times 10^{–11} \text{ Nm}^2 \text{ kg}^{–2} \))

Question. The gravitational force between the earth and an object is known as ............
Answer: Gravity or force of gravity.

Question. The gravitational force between two objects on the earth is 2 N. What will be the gravitational force between these two objects on the surface of the moon ?
Answer: Same force i.e. 2 N.

Question. Tides in oceans are formed due to gravitational force between ...........and.............
Answer: the moon, the earth.

Question. Name the force which is responsible for the revolution of planets around the sun.
Answer: Gravitational force of attraction between the planet and the sun. This force provides the necessary centripetal force to the planet to move in a circular orbit around the sun.

Question. Name the force which is responsible for the revolution of moon around the earth.
Answer: The Gravitational force between the earth and the moon provides the centripetal force to the moon to move in a circular path around the earth.

Question. How does the gravitational force between two bodies varies with r ?
Answer: \( F \propto 1/r^2 \).

Question. Is acceleration due to gravity on the surface of moon less or more than the acceleration due to gravity on the surface of earth ?
Answer: Acceleration due to gravity on the surface of the moon is less than that on the surface of the earth.

Question. Write the expression for the acceleration due to gravity. \( g = \frac{GM}{R^2} \)
Answer: \( g = \frac{GM}{R^2} \)

Question. What is the SI unit of acceleration due to gravity (g)
Answer: \( \text{ms}^{–2} \)

Question. What is the value of acceleration due to gravity on the surface of earth ?
Answer: \( g = 9.8 \text{ ms}^{–2} \)

Question. Is acceleration due to gravity a scalar or a vector quantity ?
Answer: It is a vector quantity.

Question. What is the value of acceleration due to gravity on the surface of moon ?
Answer: \( g = 1.6 \text{ ms}^{–2} \) on the surface of moon.

Question. Acceleration due to gravity on the surface of moon = ........ × Acceleration due to gravity on the surface of the earth.
Answer: \( 1/6 \)

Question. Where is the acceleration due to gravity more : at poles or at equator ?
Answer: At poles

Question. What is the value of ‘g’ at the centre of the earth ?
Answer: Zero.

Question. What will be the direction of acceleration due to gravity if the body is thrown vertically upward?
Answer: The direction of acceleration due to gravity is always towards the centre of the earth i.e. in the downward direction.

Question. Define mass of a body.
Answer: Mass of a body is defined as the quantity of matter contained in the body.

Question. Why is mass known as inertial mass ?
Answer: Since mass is a measure of the inertia of a body, so the mass is known as inertial mass.

Question. What is the SI unit of mass ?
Answer: S.I. unit of mass is kilogram

Question. Is mass of a body a scalar or a vector physical quantity.
Answer: Mass is a scalar physical quantity.

Question. The mass of a body at the equator is 20 kg. What will be the mass of this body at the poles?
Answer: 20 kg.

Question. Define weight of a body.
Answer: The force with which a body is attracted by the earth is known as the weight of the body.

Question. Write a relation between the mass and weight of the body.
Answer: \( W = mg \)

 

NUMERICAL PROBLEMS

Question. What is the gravitational acceleration of a spaceship at a distance equal to two Earth’s radius from the centre of the Earth?
Answer: \( 2.45 \text{ m/s}^2 \)

Question. A boy on a cliff 49 m high drops a stone. One second later, he throws a second stone after the ftrst. They both hit the ground at the same time. With what speed did he throw the second stone ?
Answer: \( 12.1 \text{ m/s} \)

Question. A stone drops from the edge of the roof. It passes a window 2 m high in 0·1 s. How far is the roof above the top of the window?
Answer: \( 19.4 \text{ m} \)

Question. A particle is dropped from a tower 180 m high. How long does it take to reach the ground? What is the velocity when it touches the ground? Take \( g = 10 \text{ m/s}^2 \).
Answer: \( 6 \text{ s, } 60 \text{ m/s} \)

Question. To estimate the height of a bridge over a river, a stone is dropped freely on the river from the bridge. The stone takes 2 s to touch the water surface in the river. Calculate the height of the bridge from the water level. Take \( g = 9.8 \text{ m/s}^2 \).
Answer: \( 19.6 \text{ m} \)

Question. How much would a 70 kg man weigh on moon? What will be his mass on Earth and Moon? Given g on Moon \( = 1.7 \text{ m/s}^2 \).
Answer: \( 119 \text{ N, } 70 \text{ kg, } 70 \text{ kg} \)

Question. A body has a weight of 10 kg on the surface of Earth. What will be its mass and weight when taken to the centre of Earth ?
Answer: \( 10 \text{ kg, Zero} \)

Question. A force of 2 kg wt acts on a body of mass 4·9 kg. Calculate its acceleration.
Answer: \( 4 \text{ m/s}^2 \)

Question. A force of 20 N acts upon a body whose weight is 9·8 N. What is the mass of the body and how much is its acceleration ?
Answer: \( 1 \text{ kg, } 20 \text{ m/s}^2 \)

Question. A man weighs 600 N on the Earth. What is its mass? Take \( g = 10 \text{ m/s}^2 \). If he were taken on Moon, his weight would be 100 N. What is his mass on Moon? What is acceleration due to gravity on Moon?
Answer: \( 60 \text{ kg, } 60 \text{ kg, } 1.67 \text{ m/s}^2 \)

Question. A car falls off a ledge and drops to the ground in 0·5 s. Let \( g = 10 \text{ m/s}^2 \) (for simplifying the calculations). (i) What is its speed on striking the ground? (ii) What is its average speed during 0·5 s? (iii) How high is the ledge from the ground?
Answer: (i) \( 5 \text{ m/s} \) (ii) \( 2.5 \text{ m/s} \) (iii) \( 1.25 \text{ m} \)

Question. An object is thrown vertically upwards and rises to a height of 10 m. Calculate (i) the velocity with which the object was thrown upwards and (ii) the time taken by the object to reach the highest point.
Answer: \( 14 \text{ m/s, } 1.43 \text{ s} \)

Question. Mass of an object is 10 kg. What is its weight on Earth?
Answer: \( 98 \text{ N} \)

Question. An object weighs 10 N when measured on the surface of the Earth. What would be its weight when measured on the surface of Moon ?
Answer: \( 1.67 \text{ N} \)

Question. Calculate the value of acceleration due to gravity on Moon. Given mass of Moon \( = 7.4 \times 10^{22} \text{ kg} \), radius of Moon \( = 1740 \text{ km} \).
Answer: \( 1.63 \text{ m/s}^2 \)

Question. Suppose a planet exists whose mass and radius both are half those of Earth. Calculate the acceleration due to gravity on the surface of this planet.
Answer: \( 19.6 \text{ m/s}^2 \)

Question. A ball is thrown up with a speed of 15 m/s. How high will it go before it begins to fall? Take \( g = 9.8 \text{ m/s}^2 \).
Answer: \( 11.48 \text{ m} \)

Question. How does the force of gravitation between two objects change when the distance between them is reduced to half?
Answer: \( 4F \)

Question. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?
Answer: The acceleration due to gravity is independent of the mass of the falling object.

Question. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is \( 6 \times 10^{24} \text{ kg} \) and radius of the earth is \( 6.4 \times 10^6 \text{ m} \).)
Answer: \( 9.8 \text{ N} \)