Statement A: If a particle is outside a uniform spherical shell or solid sphere with a spherically symmetric internal mass distribution, the sphere attracts the particle.
Statement B: If a particle is inside a uniform spherical shell, the gravitational force on the particle is zero.
Statement C: If a particle is inside a uniform solid sphere, the gravitational force on the particle is zero.nIn light of above statements choose the correct option.
1. Only statement C is correct
2. Only statements A and B are correct
3. Only statements C and B are correct
4. Only statements A and C are correct
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By shell theorems, the gravitational force inside a uniform spherical shell is zero (Statement B is correct) and outside it behaves like a point mass (Statement A is correct). Inside a solid sphere, the force is non-zero (Statement C is incorrect).
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
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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
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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.
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
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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).