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A body is projected up with a velocity e...

A body is projected up with a velocity equal to `sqrt((9GM)/(8R))`, where M is the mass of the earth and R is the radius of the earth. The maximum distance it reaches from the centre of the earth is

A

`(10R)/(9)`

B

`(16R)/(7)`

C

`(10R)/(3)`

D

`(9R)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let us assume that the maximum distance of the body from the centre of the earth is h.
Applying the conservation of mechanical energy, we get
`(1)/(2) m (sqrt((9GM)/(8R)))^(2)-(GM m)/(R )= -(GM m)/(h)`
`-(7)/(16) (GM m)/(R ) = -(GM m)/(h)`
`rArr h=(16R)/(7)`
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