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A particle of mass m is dropped from a g...

A particle of mass m is dropped from a great height h above the hole in the earth dug along its diameter.

A

The motion of the particle is simple harmonic

B

The motion of the particle is periodic

C

The speed of the particle at the centre of earth equals `sqrt((2GM)/((R+h)))` , where R and M are the radius and mass of the earth respectively

D

The speed of the particle at the centre of earth equals `sqrt((GM(R+3h))/(R(R+h)))`, where R and M are the radius and mass of the earth respectively

Text Solution

Verified by Experts

The correct Answer is:
D
(d) The motion is simple harmonic only inside earth. Further
`(1)/(2) mv^(2)=-(GMm)/((R+h))+(3)/(2)(GMm)/(R)`
`implies v=sqrt((GM(R-h))/(R(R+h)))`
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