Assertion (A): Earth is continuously pulling moon towards its centre but moon does not fall to earth.
Reason (R): Attraction of sun on moon is greater than that of earth on moon.
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
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Assertion (A): The Moon has sufficient tangential velocity to orbit the Earth, so it continuously 'falls around' the Earth instead of falling into it. So (A) is true.nReason (R): Calculations show that the gravitational force from the Sun on the Moon is indeed greater than that from the Earth on the Moon. So (R) is true.nHowever, the Sun's attraction does not prevent the Moon from falling to Earth; the Moon's orbital velocity does. Thus, (R) is not the correct explanation for (A).
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Angular momentum conservation can be used to explain Kepler’s second law of planetary motion.
Reason (R): Areal velocity of a planet revolving around the sun is equal to its angular momentum.
In the light of the above statements, choose the correct answer from the options given below:
1. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. Both (A) and (R) are true but (R) is not the correct explanation of (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 Kepler's second law represents the conservation of angular momentum. Reason (R) is false because areal velocity is \(\frac{dA}{dt} = \frac{L}{2m}\), which is proportional to angular momentum \(L\) but not equal to it.
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): 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
View Answer
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).