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Question

# A hole is drilled from the surface of earth to its centre. A particle is dropped from rest at the surface of earth. The speed of the particle when it reaches the centre of the earth in terms of its escape velocity on the surface of earth ve is :

A
ve2
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B
ve
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C
2ve
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D
ve2
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Solution

## The correct option is D ve√2Lets m= mass of the particleM= mass of the earthR= radius of the earthv= speed of particle when it reaches the center of the earthapplying conservation of total energy,(K.E)1+(P.E)1=(K.E)2+(P.E)20+(−GMmR)=12mv2+(−3GMm2R)−GMR+3GM2R=12v2v2=GMRv=√GMR. . . . (1)We know that the escape velocity of the particle from the earth is given by,ve=√2GMR. . . . .(2)ve=√2√GMRve=√2v (from equation 1)v=ve√2The correct option is D.

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