CBSE Class 11 Physics Gravitation Worksheet Set E

GRAVITATION

SECTION – A CONCEPTUAL AND APPLICATION TYPE QUESTIONS

Question. As observed from the earth, the sun appears to move in an approximate circular orbit. For the motion of another planet like mercury as observed from the earth, this would
(a) be similarly true
(b) not be true because the force between the earth and mercury is not inverse square law
(c) not be true because the major gravitational force on mercury is due to the sun
(d) not be true because mercury is influenced by forces other than gravitational force

Answer: C

Question. Different points in the earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the CM (centre of mass) causing translation and a net torque at the CM causing rotation around an axis through the CM. For the earth-sun system (approximating the earth as a uniform density sphere).
(a) the torque is zero
(b) the torque causes the earth to spin
(c) the rigid body result is not applicable since the earth is not even approximately a rigid body
(d) the torque causes the earth to move around the sun

Answer: A

Question. Satellites orbitting the earth have finite life and sometimes debris of satellites fall to the earth. This is because
(a) the solar cells and batteries in satellites run out
(b) the laws of gravitation predict a trajectory spiralling inwards
(c) of viscous forces causing the speed of satellite and hence height to gradually decrease
(d) of collisions with other satellites

Answer: C

Question. A cavity of radius R/2 is made inside a solid sphere of radius R. The centre of the cavity is located at a distance R/2 from the centre of the sphere. The gravitational force on a particle of mass ‘m’ at a distance R/2 from the centre of the sphere on the line joining both the centres of sphere and cavity is – (opposite to the centre of gravity) [Here g = GM/R², where M is the mass of the sphere]
(a) mg/2
(b) 3mg/8
(c) mg/16
(d) None of these

Answer: B

Question. The mass of the moon is 1/81 of earth’s mass and its radius 1/4 that of the earth. If the escape velocity from the earth’s surface is 11.2 km/sec, its value from the surface of the moon will be
(a) 0.14 kms^–1
(b) 0.5 kms^–1
(c) 2.5 kms^–1
(d) 5.0 kms^–1

Answer: C

Question. The largest and the shortest distance of the earth from the sun are r1 and r2. Its distance from the sun when it is at perpendicular to the major-axis of the orbit drawn from the sun
(a) (r₁ + r₂ ) / 4
(b) (r₁ + r₂ ) /(r₁ - r₂ )
(c) 2 r₁ r₂ /(r₁ + r₂ )
(d) (r₁ + r₂ ) /3

Answer: C

Question. Both the earth and the moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon
(a) will be elliptical
(b) will not be strictly elliptical because the total gravitational force on it is not central
(c) is not elliptical but will necessarily be a closed curve
(d) deviates considerably from being elliptical due to influence of planets other than the earth

Answer: B

Question. In our solar system, the inter-planetary region has chunks of matter (much smaller in size compared to planets) called asteroids. They
(a) will not move around the sun, since they have very small masses compared to the sun
(b) will move in an irregular way because of their small masses and will drift away into outer space
(c) will move around the sun in closed orbits but not obey Kepler's laws
(d) will move in orbits like planets and obey Kepler's laws

Answer: D

Question. Choose the wrong option.
(a) Inertial mass is a measure of difficulty of accelerating a body by an external force whereas the gravitational mass is relevant in determining the gravitational force on it by an external mass
(b) That the gravitational mass and inertial mass are equal is an experimental result
(c) That the acceleration due to gravity on the earth is the same for all bodies is due to the equality of gravitational mass and inertial mass
(d) Gravitational mass of a particle like proton can depend on the presence of neighbouring heavy objects but the inertial mass cannot

Answer: D

Question. Particles of masses 2M, m and M are respectively at points A, B and C with AB = 1/2(BC).m is much-much smaller than M and at time t = 0, they are all at rest as given in figure. At subsequent times before any collision takes place. (8 EX 3)
(a) m will remain at rest
(b) m will move towards M
(c) m will move towards 2M
(d) m will have oscillatory motion

Answer: C

Question. A body of mass ‘m’ is taken from the earth’s surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be
(a) 2/3 mgR
(b) 3 mgR
(c) 1/3 mgR
(d) mg²R

Answer: A

Question. Infinite number of bodies, each of mass 2 kg are situated on x-axis at distances 1m, 2m, 4m, 8m, ..... respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
(a) -8/3 G
(b) - 4/3 G
(c) – 4 G
(d) – G

Answer: C

Question. The radius of a planet is twice the radius of earth. Both have almost equal average mass-densities. If V_P and V_E are escape velocities of the planet and the earth, respectively, then
(a) V_E = 1.5V_P
(b) V_P = 1.5V_E
(c) V_P = 2V_E
(d) V_E = 3VP

Answer: C

Question. A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 × 10²⁴ kg) have to be compressed to be a black hole? 
(a) 10^{– 9} m
(b) 10^{– 6} m
(c) 10^–2 m
(d) 100 m

Answer: C

Question. The escape velocity from a planet is v_e. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be
(a) v_e
(b) v_e/√2
(c) v_e/2
(d) zero

Answer: B

Question. Which one of the following graphs represents correctly the variation of the gravitational field intensity (I) with the distance (r) from the centre of a spherical shell of mass M and radius a ?

Answer: D

Question. Two spherical bodies of mass M and 5 M and radii R and 2 R released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is 
(a) 4.5 R
(b) 7.5 R
(c) 1.5 R
(d) 2.5 R

Answer: B

Question. A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,
(a) the total mechanical energy of S varies periodically with time.
(b) the linear momentum of S remains constant in magnitude.
(c) the acceleration of S is always directed towards the centre of the earth.
(d) the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant.

Answer: C

Question. The ratio of escape velocity at earth (v_e) to the escape velocity at a planet (v_p) whose radius and mean density are twice as that of earth is :
(a) 1 : 2
(b) 1 : 2 √2 
(c) 1 : 4
(d) 1 : 2

Answer: B

Question. A particle of mass ‘m’ is kept at rest at a height 3R from the surface of earth, where ‘R’ is radius of earth and ‘M’ is mass of earth. The minimum speed with which it should be projected, so that it does not return back, is (g is acceleration due to gravity on the surface of earth)
(a) (GM/R)^1/2
(b) (GM/2R)^1/2
(c) (gR/4)^1/2
(d) (2g/4)1/2

Answer: B

Question. Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by: 

Answer: B

Directions for Qs. : Each question contains STATEMENT-1 and STATEMENT-2. Choose the correct answer from the following
(a) Statement -1 is false, Statement-2 is true
(b) Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1
(c) Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1
(d) Statement -1 is true, Statement-2 is false

Question. Statement -1 : Gravitational potential is maximum at infinity.
Statement -2 : Gravitational potential is the amount of work done to shift a unit mass from infinity to a given point in gravitational attraction force field.

Answer: B

Question. Statement -1 : For the planets orbiting around the sun, angular speed, linear speed and K.E. changes with time, but angular momentum remains constant.
Statement -2 : No torque is acting on the rotating planet. So its angular momentum is constant.

Answer: B

1. Distinguish between gravity and gravitation.

2. What is the weight of a body at the centre of earth?

3. What is relation between orbital and escape velocity?

4. Distinguish between inertial and gravitational mass?

5. What are conditions for a satellite to appear stationary?

6. Why do different planets have different escape velocities?

7. A satellite is in circular orbit of radius r. Another satellite is in circular orbit of radius 4r. How do you compare their orbital velocities?

8. Does a planet revolving around sun in an elliptical orbit have a constant (i) linear speed (ii) angular momentum (iii) kinetic energy (iv) potential energy and (v) total energy throughout its orbit?

SECTION-B NUMERICAL QUESTIONS

1. A rocket is fired from the earth towards the sun. At what point on its path is the gravitational force on the rocket zero? Mass of sun = 2x 10³⁰kg, mass of the earth = 6x 10²⁴kg. Neglect the effect of other planets etc. Orbital radius = 1.5x 10¹¹m.

2. A body weights 90 kgf on the surface of the earth. How much will it weigh on the surface of Mars whose mass is 1/9 and the radius is 1/2 of that of the earth?

3. At what height from the surface of the earth, will the value of g be reduced by 36% from the value at the surface? Radius of the earth = 6400km.

4. A body weighs 63N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

5. A remote sensing satellite of the earth revolves in a circular at a height of 250 km above the earth’s surface. What is the (i) orbital speed and (ii) period of revolution of the satellite? Radius of the earth = 6400 km.

6. Determine the escape velocity of a body from moon. Take the moon to be a uniform sphere of radius 1.76x 10⁶m, and mass 7.36x 10²²kg. Given G = 6.67 X 10-11Nm²kg^-2.

7. The escape velocity of a projectile on earth’s surface is 11.2 kms^-1. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun other planets.

8. Calculate the period of revolution of Neptune around the sun, given that diameter of its orbit is 30 times the diameter of earth’s orbit around the sun, both orbits being assumed to be circular.

9. A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.5 x 10⁸km away from the sun?

10. Find the potential energy of a system of four particles of equal masses M placed at the corners of a square of side L. Also obtain potential at the centre of the square.

11. Compare the period of revolution of a planet around the sun with that of the earth around the sun. The mean distance of the planet from the sun is 1.52 AU

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