JEE Physics Gravitation MCQs Set 07

Physics Objective Questions and Answers: Gravitation

Access targeted multiple-choice questions for Gravitation designed to align with the latest JEE academic syllabus for JEE Physics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Download Gravitation MCQs with Answers

Access the complete set of multiple-choice questions for Gravitation below. This focused format allows students to isolate specific topics for thorough review and uninterrupted practice alongside official JEE textbooks.

Multiple Choice Questions

Question 1: Two satellites of the same mass m revolve round the earth (mass M) in the same orbit of radius r but in opposite directions, so they can collide. The total mechanical energy of the system (both satellites and the earth, m much less than M) is:
(a) \( -\frac{GMm}{r} \)
(b) \( -\frac{2GMm}{r} \)
(c) \( -\frac{GMm}{2r} \)
(d) zero
Show Answer & Explanation

Answer: (a) \( -\frac{GMm}{r} \)

Explanation:
1. Each satellite has \( -\frac{GMm}{2r} \)
2. Total \( = -\frac{GMm}{r} \)

Teacher's Note:
1. Energy does not depend on direction of revolution.

Question 2: A planet of mass m moves in an elliptical orbit about the sun (mass M). The maximum and minimum distances from the sun are r1 and r2. The period of revolution is proportional to:
(a) \( r_1^{1/2} \)
(b) \( r_2^{3/2} \)
(c) \( (r_1-r_2)^{3/2} \)
(d) \( (r_1+r_2)^{3/2} \)
Show Answer & Explanation

Answer: (d) \( (r_1+r_2)^{3/2} \)

Explanation:
1. \( T \propto a^{3/2} \) with \( a = \frac{r_1+r_2}{2} \)
2. So \( T \propto (r_1+r_2)^{3/2} \)

Teacher's Note:
1. Semi-major axis is the average of the extreme distances.

Question 3: A relay satellite transmits television programmes continuously from one part of the world to another because its:
(a) period is greater than the period of rotation of the earth about its axis
(b) period is less than the period of rotation of the earth about its axis
(c) period is equal to the period of rotation of the earth about its axis
(d) mass is less than the mass of the earth
Show Answer & Explanation

Answer: (c) period is equal to the period of rotation of the earth about its axis

Explanation:
1. It is a geostationary satellite
2. Equal period means it stays above the same point

Teacher's Note:
1. Period must be 24 hours.

Question 4: A satellite is stopped suddenly in its orbit at a distance equal to the earth's radius from the earth's surface and allowed to fall freely. The speed with which it hits the earth's surface is:
(a) 7.919 m/s
(b) 7.919 km/s
(c) 11.2 m/s
(d) 11.2 km/s
Show Answer & Explanation

Answer: (b) 7.919 km/s

Explanation:
1. \( \frac12v^2 = GM\left(\frac1R-\frac1{2R}\right) = \frac{GM}{2R} \)
2. \( v = \sqrt{\frac{GM}{R}} = 7.9 \) km/s

Teacher's Note:
1. Initial distance from centre is 2R.

Question 5: A planet moves in an elliptical orbit. T, U, E and L are its kinetic energy, potential energy, total energy and magnitude of angular momentum. Which statement is true?
(a) T is conserved
(b) U is always positive
(c) E is always negative
(d) L is conserved but the direction of vector L will continuously change
Show Answer & Explanation

Answer: (c) E is always negative

Explanation:
1. Kinetic energy changes along the orbit
2. Potential energy is negative
3. E is negative for bound orbits
4. L is conserved in both magnitude and direction

Teacher's Note:
1. A bound orbit has total energy below zero.

Question 6: The gravitational force between two bodies is proportional to \( \frac1R \) (not \( \frac1{R^2} \)), where R is the distance. The orbital speed in a circular orbit for this force is proportional to:
(a) \( 1/R^2 \)
(b) \( R^0 \)
(c) \( R \)
(d) \( 1/R \)
Show Answer & Explanation

Answer: (b) \( R^0 \)

Explanation:
1. \( \frac{mv^2}{R} = \frac kR \)
2. \( v^2 = k/m \), independent of R

Teacher's Note:
1. Speed is the same in all orbits.

Question 7: The velocity of a satellite revolving around the earth at a height h above the surface (radius of earth R) is:
(a) \( R^2\sqrt{\frac{g}{R+h}} \)
(b) \( R\frac{g}{(R+h)^2} \)
(c) \( R\sqrt{\frac{g}{R+h}} \)
(d) \( R\sqrt{\frac{R+h}{g}} \)
Show Answer & Explanation

Answer: (c) \( R\sqrt{\frac{g}{R+h}} \)

Explanation:
1. \( v = \sqrt{\frac{GM}{R+h}} \) with \( GM = gR^2 \)
2. \( v = R\sqrt{\frac{g}{R+h}} \)

Teacher's Note:
1. Use GM = gR squared.

Question 8: Two artificial satellites of masses m1 and m2 move with speeds v1 and v2 in orbits of radii r1 and r2 with r1 > r2. Then:
(a) v1 = v2
(b) v1 > v2
(c) v1 < v2
(d) \( v_1/r_1 = v_2/r_2 \)
Show Answer & Explanation

Answer: (c) v1 < v2

Explanation:
1. \( v \propto r^{-1/2} \)
2. Larger radius gives smaller speed

Teacher's Note:
1. Orbital speed is independent of mass.

Question 9: The orbital radius of a satellite S of the earth is four times that of a communication (geostationary) satellite C. The period of revolution of S is:
(a) 4 days
(b) 8 days
(c) 16 days
(d) 32 days
Show Answer & Explanation

Answer: (b) 8 days

Explanation:
1. \( T \propto r^{3/2} \)
2. \( T_S = 1\times4^{3/2} = 8 \) days

Teacher's Note:
1. Geostationary period is 1 day.

Question 10: If a satellite revolves very close to the earth's surface, its orbital velocity does not depend upon:
(a) the mass of the satellite
(b) the mass of the earth
(c) the radius of the earth
(d) the orbital radius
Show Answer & Explanation

Answer: (a) the mass of the satellite

Explanation:
1. \( v = \sqrt{GM/R} \)
2. Satellite mass cancels

Teacher's Note:
1. Orbital velocity is independent of the satellite's mass.

Question 11: Two identical satellites are at heights R and 7R from the earth's surface (R = radius of the earth). Which statement is incorrect?
(a) The ratio of total energy of both is 5
(b) The ratio of kinetic energy of both is 4
(c) The ratio of potential energy of both is 4
(d) The ratio of total energy of both is 4
Show Answer & Explanation

Answer: (a) The ratio of total energy of both is 5

Explanation:
1. Orbit radii are 2R and 8R, ratio 4
2. \( K \), \( U \) and \( E \) are each proportional to \( 1/r \)
3. All three ratios are 4, so the ratio 5 is incorrect

Teacher's Note:
1. Energy ratios follow the inverse orbital radius.

Question 12: The minimum projection velocity of a body from the earth's surface so that it becomes a satellite of the earth (R = 6.4 x 10^6 m) is about:
(a) \( 11\times10^3 \) m/s
(b) \( 8\times10^3 \) m/s
(c) \( 6.4\times10^3 \) m/s
(d) \( 4\times10^3 \) m/s
Show Answer & Explanation

Answer: (b) \( 8\times10^3 \) m/s

Explanation:
1. \( v = \sqrt{gR} = \sqrt{9.8\times6.4\times10^6} \approx 7.9\times10^3 \) m/s

Teacher's Note:
1. This is the first cosmic velocity.

Question 13: A geostationary satellite:
(a) is situated at a great height above the surface of the earth
(b) moves in the equatorial plane
(c) has a time period of 24 hours
(d) has a time period of 24 hours and moves in the equatorial plane
Show Answer & Explanation

Answer: (d) has a time period of 24 hours and moves in the equatorial plane

Explanation:
1. It must orbit in the equatorial plane
2. With period equal to one sidereal day, it stays over one point

Teacher's Note:
1. Both conditions are needed for a geostationary orbit.

Question 14: The maximum and minimum distances of a comet from the sun are \( 8\times10^{12} \) m and \( 1.6\times10^{12} \) m. If its speed when nearest to the sun is 60 m/s, its speed in m/s when farthest is:
(a) 12
(b) 60
(c) 112
(d) 6
Show Answer & Explanation

Answer: (a) 12

Explanation:
1. Angular momentum conservation: \( v_1r_1 = v_2r_2 \)
2. \( v = 60\times\frac{1.6\times10^{12}}{8\times10^{12}} = 12 \) m/s

Teacher's Note:
1. Product of speed and distance is constant at the extremes.

Question 15: A satellite of mass m goes round the earth along a circular path of radius r. If m_E is the mass of the earth and R_E its radius, the linear speed of the satellite depends on:
(a) \( m, m_E \) and \( r \)
(b) \( m, R_E \) and \( r \)
(c) \( m_E \) only
(d) \( m_E \) and \( r \)
Show Answer & Explanation

Answer: (d) \( m_E \) and \( r \)

Explanation:
1. \( v = \sqrt{\frac{Gm_E}{r}} \)

Teacher's Note:
1. Independent of the satellite mass and earth radius.

Question 16: Near the earth's surface the time period of a satellite is 1.4 hours. Its time period at a distance 4R from the centre of the earth is about:
(a) 32 hours
(b) \( \frac{1}{8\sqrt2} \) hours
(c) \( 8\sqrt2 \) hours
(d) 16 hours
Show Answer & Explanation

Answer: (c) \( 8\sqrt2 \) hours

Explanation:
1. \( T \propto r^{3/2} \)
2. \( T = 1.4\times4^{3/2} = 11.2 \) hours
3. \( 8\sqrt2 = 11.3 \), the nearest option

Teacher's Note:
1. Radius becomes four times the near-surface orbit.

Question 17: A communication satellite of the earth with a period of 24 hours has to be replaced by another satellite of double mass. If the new satellite also has a period of 24 hours, the ratio of the radius of the new orbit to the original orbit is:
(a) 1 : 1
(b) 2 : 1
(c) \( \sqrt2 : 1 \)
(d) 1 : 2
Show Answer & Explanation

Answer: (a) 1 : 1

Explanation:
1. \( T^2 = \frac{4\pi^2r^3}{GM} \) has no satellite mass
2. Same T gives same r

Teacher's Note:
1. Orbit radius does not depend on the satellite's mass.

Question 18: Escape velocity for a projectile at the earth's surface is V_e. A body is projected from the earth's surface with velocity 2V_e. Its velocity at infinite distance is:
(a) \( V_e \)
(b) \( 2V_e \)
(c) \( \sqrt2V_e \)
(d) \( \sqrt3V_e \)
Show Answer & Explanation

Answer: (d) \( \sqrt3V_e \)

Explanation:
1. \( \frac12v^2 = \frac12(2V_e)^2 - \frac12V_e^2 \)
2. \( v^2 = 3V_e^2 \)
3. \( v = \sqrt3V_e \)

Teacher's Note:
1. Subtract escape energy from initial kinetic energy.

Question 19:
Assertion (A): The gravitational field of the moon is much less than that of the earth.
Reason (R): The gravitational field of a given mass M depends on M/r², which is smaller for the moon.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Moon's M/R² is about one sixth of the earth's
2. R gives the formula that explains A

Teacher's Note:
1. The moon's surface field is about 1.6 N/kg.
2. Field depends on mass and radius.

Question 20:
Assertion (A): If an earth satellite moves to a lower orbit, there is some dissipation of energy but the satellite speed increases.
Reason (R): The speed of a satellite is a constant quantity.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (c) A is true, but R is false.

Explanation:
1. Lower orbit means higher speed, so A is true
2. Speed varies with orbit radius, so R is false

Teacher's Note:
1. Energy loss lowers the orbit and increases the speed.
2. Orbital speed is not constant across orbits.

Question 21:
Assertion (A): If the gravitational force is proportional to 1/R³, then Kepler's second law would not be affected.
Reason (R): For Kepler's second law, the central nature of the force is the only condition.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. Areal velocity is constant for any central force
2. So the law of areas still holds and R explains A

Teacher's Note:
1. Angular momentum is conserved for any central force.
2. The inverse-square form matters only for the third law.

Question 22:
Assertion (A): The angular momentum of a satellite remains conserved.
Reason (R): Conservation of linear momentum leads to conservation of angular momentum.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (c) A is true, but R is false.

Explanation:
1. Gravity is central, so angular momentum is conserved and A is true
2. Linear momentum is not conserved here, and the two conservation laws are independent, so R is false

Teacher's Note:
1. Angular momentum conservation arises from zero torque.
2. Linear momentum changes under the central force.

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Practice MCQs for JEE Physics Gravitation

Download Multiple Choice Questions: Gravitation (JEE Physics)

Test your conceptual understanding of Gravitation with these targeted multiple-choice questions. Designed in alignment with the latest JEE curriculum for JEE Physics, these problem sets build accuracy and prepare students for objective exams.

Concept Clarification for Gravitation

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