Assertion (A): The mechanical energy of earth-moon system remains same when a heavenly body passes nearby the earth-moon system.
Reason (R): Force exerted by heavenly body on the earth-moon system is non-conservative.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is false:
An external heavenly body exerts a gravitational force on the Earth-Moon system, causing its mechanical energy to change.
Reason (R) is false: Gravitational force is a conservative force by nature. Therefore, both Assertion (A) and Reason (R) are false.
Assertion (A): Comets move around the sun in elliptical orbits. The gravitational force on the comet due to sun is not normal to the comet’s velocity but the work done by the gravitation force over every complete orbit of the comet is zero.
Reason (R): Gravitational force is a conservative force.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Gravitational force is a conservative force. For a conservative force, the work done over a closed path (like a complete elliptical orbit) is zero.
Therefore, both Assertion and Reason are true, and Reason is the correct explanation of the Assertion.
Assertion (A): An artificial satellite is moving in a circular orbit of the earth. If the gravitational pull suddenly disappears, then it moves with the same speed tangential to the original orbit.
Reason (R): The orbital speed of a satellite decreases with the increase in radius of the orbit.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true due to inertia (Newton's First Law). Reason (R) is true as orbital speed \(v = \sqrt{GM/r}\) decreases with increasing \(r\).
However, R does not explain A; A is a consequence of inertia, not the relation between orbital speed and radius.
Assertion (A): If a body is taken from earth to moon, its gravitational mass becomes one-sixth on moon.
Reason (R): Gravitational mass depends upon acceleration due to gravity.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Mass is an intrinsic property of a body and does not change with location or acceleration due to gravity. Only weight \(W = mg\) changes. Therefore, both Assertion (A) and Reason (R) are false.
Assertion (A): A person in an artificial satellite revolving around the earth feels weightlessness.
Reason (R): There is no gravitational force on the satellite.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true because weightlessness in orbit is due to continuous freefall. Reason (R) is false; gravitational force *is* present and provides the centripetal force for orbit.
Assertion (A): A spherically symmetric shell produces no gravitational field anywhere.
Reason (R): The field due to various mass elements cancel out, everywhere for a spherically symmetric shell.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
A spherically symmetric shell produces zero gravitational field *inside* itself, but a non-zero field *outside*. Thus, "anywhere" and "everywhere" make both Assertion (A) and Reason (R) are false.
Assertion (A): The plane of the orbit of an artificial satellite must contain the centre of the earth.
Reason (R): For the orbital motion of satellite, the necessary centripetal force is provided by gravitational pull of earth on satellite.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Both Assertion (A) and Reason (R) are true. The gravitational force being a central force (R) ensures angular momentum conservation, which mandates that the orbital plane must contain the center of the earth (A).
Assertion (A): Escape velocity of a satellite is greater than its orbital velocity.
Reason (R): Orbit of a satellite is within the gravitational field of planet whereas escaping is beyond the gravitational field of planet.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: escape velocity \(V_e = \sqrt{2GM/r}\) is \(\sqrt{2}\) times orbital velocity \(V_o = \sqrt{GM/r}\) for a circular orbit.
Reason (R) is false because the gravitational field extends infinitely. Escaping means overcoming the gravitational potential, not leaving the field.
Assertion (A): Escape velocity from surface of a planet is \(V_e\). If a tunnel is made inside the surface, the escape velocity from a point inside the tunnel must be greater than \(V_e\).
Reason (R): Gravitational force is a conservative central force.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true; the gravitational potential energy is more negative (deeper well) inside a uniform planet, requiring greater escape velocity.
Reason (R) is true and foundational: gravity being a conservative central force allows the definition and calculation of potential energy and escape velocity.
Assertion (A): Total energy is conserved in moving a satellite to higher orbit.
Reason (R): Sum of change in potential energy and kinetic energy is same in magnitude and opposite in nature.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is false; moving a satellite to a higher orbit requires external work, increasing its total energy. Reason (R) is false in this context; \(\Delta K = -\Delta U\) applies only when mechanical energy is conserved, which is not the case when external work is done.