Velocity.of a body released from a distanced measured from the centre of earth of mass M and radius R when
it strikes the surface of earth is given by v is

Options

A. `"GM"(1/d-(1)/(R))`
B. `sqrt(2"GM"(1/R-(1)/(d)))`
C. `sqrt(3"GM"(1/R-(1)/(d)))`
D. `2"GM"(1/d-(1)/(R))`

Answer

B

Explanation

At the time of rest
Total energy = KE +P E =0+ `("GMm")/(d)" ".........(i)`
On reaching the ground `E_(r)=(1)/(2)"mv"^(2)-("GMm")/(R)" "......(ii)`
Equating (i) and (ii) `v=sqrt(2"GM"(1/R-(1)/(d)))`