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A projectile is fired vertically upwards...

A projectile is fired vertically upwards from the surface of the earth with a velocity `Kv_(e)`, where `v_(e)` is the escape velocity and `Klt1`.If `R` is the radius of the earth, the maximum height to which it will rise measured from the centre of the earth will be (neglect air resistance)

A

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

B

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

C

`R(1-k^(2))`

D

`(R)/(1+k^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
If a body is projected from the surface of the earth with a velocity v and reaches a height h, then according to the law of conservation of energy,
`(1)/(2)mv^(2) =(mgh)/(1+(h)/(R))`
Here, `v = kv_(e) = k sqrt(2gR)`
`:. (1)/(2)mk^(2) 2gR = (mg(r-R))/(1+((r-R))/(R))`
`k^(2)R[1+(r-R)/(R)] = r-R`
or `k^(2)r =r -rR`
or `r = (R)/(1-k^(2))`
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