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A projectile is fired from earth vertica...

A projectile is fired from earth vertically with a velocity `Kv_(e )` where `v_(e )=` escape velocity and K is a constant less than unity. What is the maximum height to which it rises as measured from centre of earth?

A

`(R )/(K^(2))`

B

`(R )/(1-K^(2))`

C

`(R )/(K^(2)-1)`

D

`(K^(2)R)/(R-1)`

Text Solution

Verified by Experts

The correct Answer is:
B

Let r be the maximum distance from the centre of earth to which projectile rises, then,
`(1)/(2)mk^(2)v_(e )^(2)=(GMm)/(R )-(GMm)/(r )`
`(1)/(2) mk^(2)(2GM)/(R )=GMm[(1)/(R )-(1)/(r )]`
`(1)/(r )=(1)/(R )-(k^(2))/(R )=(1-k^(2))/(R )`
or `r=(R )/(1-k^(2))`.
Correct choice is (b).
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