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
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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): Two satellites A and B are in the same orbit around the earth, B being behind A. Satellite B can overtake satellite A by increasing its speed.
Reason (R): Orbital speeds of two satellite in same orbit may different
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. For a satellite to remain in a given orbit, its speed must be constant. Increasing speed will cause the satellite to move to a higher orbit or escape. Reason (R) is false. Satellites in the same orbit must have the same orbital speed to maintain that orbit. Therefore, both (A) and (R) are false.
Assertion (A): At the centre of the earth, a body has centre of mass, but no centre of gravity.
Reason (R): Acceleration due to gravity is zero at the centre of the earth.
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. A body always has a center of mass.
Centre of gravity is the point where the net gravitational torque is zero. At the center of the Earth, the acceleration due to gravity \( g \) is zero. Thus, there is no gravitational force, and consequently, no center of gravity in the usual operational sense.
Reason (R) is true. The acceleration due to gravity \( g \) is indeed zero at the centre of the earth. Since the absence of gravity leads to no definable centre of gravity, (R) is the correct explanation for (A).
Assertion (A): The mechanical energy of earth-moon system remains same when another 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
View Answer
Assertion (A) is false.
If another heavenly body passes nearby, it exerts an external gravitational force on the earth-moon system. This external force can do work, changing the system's total mechanical energy.
Reason (R) is false. Gravitational force is a conservative force, not non-conservative. Therefore, both (A) and (R) are false.
Assertion (A): An astronaut in an orbiting space station above the earth experiences weightlessness.
Reason (R): An object orbiting around the earth under the influence of the earth’s gravitational force is in a state of free fall.
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.
Astronauts in an orbiting space station experience apparent weightlessness because they, along with the station, are continuously falling towards the Earth.
Reason (R) is true. Orbiting is a continuous state of free fall where the object's tangential velocity prevents it from hitting the Earth. (R) correctly explains (A) because weightlessness is a direct consequence of being in a constant state of free fall.
Assertion (A): Gravitational potential of earth at every place upon it is negative.
Reason (R): Every body on earth is bound by the attraction of earth.
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. Gravitational potential is defined as the work done to bring a unit mass from infinity (where potential is zero) to a point. Since gravity is attractive, this work is done by the field, resulting in negative potential. Reason (R) is true. All bodies on Earth are held by Earth's gravitational attraction, thus are gravitationally bound. The negative gravitational potential signifies that objects are bound in the gravitational field, so (R) is a correct explanation for (A).
Assertion (A): For a system of masses at some finite distance, gravitational field can be zero but gravitational potential can not be zero.
Reason (R): Gravitational field is a scalar quantity while gravitational potential is a vector quantity.
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. Gravitational field is a vector quantity, so fields from multiple masses can cancel out at certain points (e.g., between two equal masses). Gravitational potential, being a scalar sum of negative values \( V = \sum ( -\frac{Gm_i}{r_i}) \) for positive masses, can never be zero at a finite distance (only at infinity). Reason (R) is false. Gravitational field is a vector quantity, while gravitational potential is a scalar quantity. Thus, (A) is true but (R) is false.
Assertion (A): Period of revolution of satellite in circular orbit around earth is inversely proportional to cube of its orbital speed.
Reason (R): Period of revolution in uniform circular motion is given by \( T = \frac{2\pi r}{v} \) where \( r \) is radius of orbit and \( v \) is speed.
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. For a satellite in circular orbit, orbital speed \( v = \sqrt{\frac{GM}{r}} \) implying \( r \propto \frac{1}{v^2} \). The period is \( T = \frac{2\pi r}{v} \). Substituting \( r \), we get \( T \propto \frac{1/v^2}{v} \propto \frac{1}{v^3} \).
Reason (R) is true. The formula \( T = \frac{2\pi r}{v} \) is the correct definition for the period of uniform circular motion. However, (R) is a kinematic definition and does not explain the dynamic relationship between \( T \) and \( v \) for a satellite, which requires considering gravity. Thus, (R) is not the correct explanation of (A).
Assertion (A): Assuming zero potential at infinity, the gravitational potential at a point can never be positive.
Reason (R): The magnitude of gravitational force between two particles has inverse square dependence on the distance between two particles.
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. For physical masses (which are always positive), gravitational potential is given by \( V = -\frac{GM}{r} \). Since G, M, and r are positive, V must always be negative (or zero at infinity). Reason (R) is true. The gravitational force follows Newton's inverse square law, \( F = \frac{GMm}{r^2} \). This inverse square law, combined with the attractive nature of gravity, ensures that the potential energy and thus the gravitational potential remain negative when potential at infinity is set to zero. Thus, (R) is the correct explanation for (A).
Assertion (A): Gravitational field of a uniform spherical shell outside it is same as that of particle of same mass placed at its centre of mass.
Reason (R): For the calculation of gravitational force between any two uniform spherical shells, they can always be replaced by particles of same mass placed at respective centres.
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 as per Newton's Shell Theorem, a uniform spherical shell behaves like a point mass at its center for external points. Reason (R) is also true and is the basis for simplifying calculations of gravitational forces between spherical objects. Hence, (R) correctly explains (A).