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A particle is projected vertically upwar...

A particle is projected vertically upwards the surface of the earth (radius `R_(e))` with a speed equal to one fourth of escape velocity what is the maximum height attained by it from the surface of the earth?

A

`(16)/(15)R_(e)`

B

`(R_(e))/(15)`

C

`(4)/(15)R_(e)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
From conservation of mechanical energy `(1)/(2)mv^(2)=(GMm)/(R_(e))-(GMm)/(R)`
Where `R=` maximum distance from centre of the earth also `v=(1)/(4)v_(e)=(1)/(4)sqrt((2GM)/(R_(e)))`
`implies(1)/(2)mxx(1)/(16)xx(2GM)/(R_(e))=(GMm)/(R_(e))-(GMm)/(R)impliesR=(16)/(15)R_(e)impliesh=R-R_(e)=(R_(e))/(15)`.
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