Assertion (A): Moon revolving around earth does not come closer despite earth’s gravitational attraction.
Reason (R): A radially outward force balances earth’s force of attraction during revolution of moon.
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 Moon maintains a stable orbit around Earth. Reason (R) is false. There is no radially outward force balancing Earth's gravity. Instead, Earth's gravitational force *is* the centripetal force required for the Moon's orbit. The Moon's tangential velocity prevents it from falling directly into Earth while gravity pulls it in.
Assertion (A): If the law of gravitation, instead of being inverse square law then planets will still have elliptical orbits.
Reason (R): In that case also, \( T^2 \propto r^3 \) (symbols having usual meanings)
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. Only an inverse-square force leads to stable, closed elliptical orbits. An inverse cube law would lead to unstable orbits. Reason (R) is also false. Kepler's third law, \( T^2 propto r^3 \), is a direct consequence of the inverse-square law. If the law changes, this relation no longer holds. Therefore, both (A) and (R) are false.
Assertion (A): Even when orbit of a satellite is elliptical, its plane of rotation passes through the centre of earth.
Reason (R): According to law of conservation of angular momentum plane of rotation of satellite always remain same.
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): For any central force, the orbit is always planar and contains the center of force (Earth's center). So (A) is true.
Reason (R): Gravitational force is a central force, so net torque is zero. This implies conservation of angular momentum, \(\vec{L} = \vec{r} \times \vec{p}\), which means the orbital plane is fixed. So (R) is true. (R) correctly explains (A).
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).
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): 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): 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): 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): Comet tail points away from the sun.
Reason (R): Solar radiation vapourise the volatile materials within the comet.
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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The comet tail always points away from the Sun due to solar wind and radiation pressure pushing on the sublimated material. Solar radiation does vaporize volatile materials, forming the tail, but this vaporization itself doesn't fully explain the direction. Hence, both statements are true, but R is not the correct explanation of A.