JEE Advanced (Assertion-Reason Type): Gravitation | Chapter-wise Tests for JEE Main & Advanced PDF Download

Directions : Each of these questions contain two statements, Assertion and Reason. Each of these questions also has alternative choices, only one of which is the correct answer.
Q.1. Assertion : A body becomes massless at the centre of earth.
Reason : This follows from g’ = g (1 – d/R)
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (d)
At the centre of the earth, weight is zero but mass cannot be and never zero.

Q.2. Assertion : Moon travellers tie heavy weight at their back before landing on the moon.
Reason : The acceleration due to gravity on moon is smaller than that of earth.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (a)
To counter balance the effect of gravity.

Q.3. Assertion : Gravitational potential of earth at every place on it is negative.
Reason : Every body on earth is bound by the attraction of earth.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (a)
Because gravitational force is always attractive in nature and every body is bound by this gravitational force of attraction of earth.

Q.4. Assertion: Planets appear to move slower when they are farther from the sun than when they are nearer.
Reason: All planets move in elliptical orbits with sun at one of the foci of the ellipse.
(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Correct Answer is option (b)
Both assertion and reason are true, but reason is not correct explanation of the assertion.

Q.5. Assertion: Smaller the orbit of the planet around the sun, shorter is the time it takes to complete one revolution.
Reason: According to Kepler's third law of planetary motion, square of time period is proportional to cube of mean distance from sun.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (b)
According to Kepler's third law T² ∝ r³. If r is small then T will also be small.

Q.6. Assertion: The value of acceleration due to gravity does not depend upon mass of the body on which force is applied.
Reason: Acceleration due to gravity is a constant quantity.

(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (c)
Acceleration due to gravity is given by g = GM/R². Thus it does not depend on mass of body on which it is acting. Also it is not a constant quantity it changes with change in value of both M and R (distance between two bodies).

Q.7. Assertion: If earth suddenly stops rotating about its axis, then the value of acceleration due to gravity will become same at all the places.
Reason: The value of acceleration due to gravity is independent of rotation of earth.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (c)
The value of g at any place is given by the relation, g′ = g − ω² R_ecos²λ. When l is angle of latitude and w is the angular velocity of earth. If earth suddenly stops rotating, then ω = 0 \ g′ = g i.e., the value of g will be same at all places.

Q.8. Assertion: There is no effect of rotation of earth on acceleration due to gravity at poles.
Reason: Rotation of earth is about polar axis.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (a)
As the rotation of earth takes place about polar axis therefore body placed at poles will not feel any centrifugal force and its weight or acceleration due to gravity remains unaffected.

Q.9. Assertion: A force act upon the earth revolving in a circular orbit about the sun. Hence work should be done on the earth.
Reason: The necessary centripetal force for circular motion of earth comes from the gravitational force between earth and sun.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (e)
Earth revolves around the sun in circular path and required centripetal force is provided by gravitational force between earth and sun but the work done by this centripetal force is zero.

Q.10. Assertion: The ratio of inertial mass to gravitational mass is equal to one.
Reason: The inertial mass and gravitational mass of a body are equivalent.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (a)
Inertial mass and gravitational mass are equivalent. Both are scalar quantities and measured in the same unit. They are quite different in the method of their measurement. Also gravitational mass of a body is affected by the presence of other bodies near it where as internal mass remain unaffected.

Q.11. Assertion: Gravitational potential of earth at every place on it is negative.
Reason: Every body on earth is bound by the attraction of earth.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (a)
Because gravitational force is always attractive in nature and every body is bound by this gravitational force of attraction of earth.

Q.12. Assertion: Even when orbit of a satellite is elliptical, its plane of rotation passes through the centre of earth.
Reason: According to law of conservation of angular momentum plane of rotation of satellite always remain same.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (a)
As no torque is acting on the planet, its angular momentum must remain constant in magnitude as well as direction. Therefore, plane of rotation must pass through the centre of earth.

Q.13. Assertion: A planet moves faster, when it is closer to the sun in its orbit and vice versa.
Reason: Orbital velocity in orbital of planet is constant.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (a)
According to Kepler's law of planetary motion, a planet revolves around the sun in such a way that its areal velocity is constant. i.e., it move faster, when it is closer the sun and vice-versa.

Q.14. Assertion: Orbital velocity of a satellite is greater than its escape velocity.
Reason: Orbit of a satellite is within the gravitational field of earth whereas escaping is beyond the gravitational field of earth.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (e)
Escape velocity = √2 × orbital velocity.

Q.15. Assertion: If an earth satellite moves to a lower orbit, there is some dissipation of energy but the satellite speed increases.
Reason: The speed of satellite is a constant quantity.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (c)
Due to resistance force of atmosphere, the satellite revolving around the earth losses kinetic energy. Therefore in a particular orbit the gravitational attraction of earth on satellite becomes greater than that required for circular orbit there. Therefore satellite moves down to a lower orbit. In the lower orbit as the potential energy (U = −GMm/r) becomes more negative, Hence kinetic energy (E_K = GMm/2r) increases, and hence speed of satellite increases.

Q.16. Assertion: Earth has an atmosphere but the moon does not.
Reason: Moon is very small in comparison to earth.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (b)
If root mean square velocity of the gas molecules is less than escape velocity from that planet (or satellite) then atmosphere will remain attached with that planet and if v_rms > v_escape then there will be no atmosphere on the planet. This is the reason for no atmosphere at moon.

Q.17. Assertion: The time period of geostationary satellite is 24 hours.
Reason: Geostationary satellite must have the same time period as the time taken by the earth to complete one revolution about its axis.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (b)
As the geostationary satellite is established in an orbit in the plane of the equator at a particular place, so it move in the same sense as the earth and hence its time period of revolution is equal to 24 hours, which is equal to time period of revolution of earth about its axis.

Q.18. Assertion: Two different planets have same escape velocity.
Reason: Value of escape velocity is a universal constant.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (d)
As, escape velocity =, so its value depends on mass of planet and radius of the planet. The two different planets have same escape velocity, when these quantities (mass and radius) are equal.

Q.19. Assertion: Generally the path of a projectile from the earth is parabolic but it is elliptical for projectiles going to a very large height.
Reason: The path of a projectile is independent of the gravitational force of earth.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (c)
Upto ordinary heights, the change in the distance of a projectile from the centre of earth is negligible compared to the radius of earth. Hence the projectile moves under a nearly uniform gravitational force and the path is parabolic. But for the projectiles moving to a large height, the gravitational force decreases quite decreasing variable force, the path of the projectile becomes elliptical.

Q.20. Assertion: Space rockets are usually launched in the equatorial line from west to east.
Reason: The acceleration due to gravity is minimum at the equator.
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

Correct Answer is option (b)
We know that earth revolves from west to east about its polar axis. Therefore, all the particles on the earth have velocity from west to east. This velocity is maximum in the equatorial line, as v = Rω, where R is the radius of earth and w is the angular velocity of revolution of earth about its polar axis. When a rocket is launched from west to east in equatorial plane, the maximum linear velocity is added to the launching velocity of the rocket, due to which launching becomes easier.