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Question

# Assertion :In free space a uniform spherical planet of mass M has a smooth narrow tunnel along its diameter. This planet and another superdense small particle of mass M start approaching towards each other from rest under action of their gravitational forces. When the particle passes through the centre of the planet, sum of kinetic energies of both the bodies is maximum. Reason: When the resultant of all forces acting on a particle or a particle like object (initially at rest) is constant in direction, the kinetic energy of the particle keeps on increasing.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

## The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionDue to the gravitational force acts on these two bodies, the speed of each component of the system increases due to loss in potential energy. It only increases, however, upto the time the particle reaches the center of planet. After that point, the net force exerted by them on each other reverses its direction. Due to this reversal, the speed of each component of the system starts decreasing and hence the kinetic energy. Thus the kinetic energy is maximum at the center.

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