A bullet is fired vertically upwards with velocity v form the surface of a spherical planet. If the escape velocity from the planet is `v_(esc) = vsqrtN`, then the value of N is (ignore energy loss due to atmosphere)

Answer

B

Explanation

Let h be the height to which the bullet rises
`then, g^1 =g((1+(h)/(R ))^(-2)`
`rArr (g)/(4) = g((1 +(h)/(R )^(-2)`
`rArr h =R`
we know that `v_e = sqrt((2GM)/(R ) = vsqrtN (given) …(i)`
Now applying conservation of energy for the throw
loss of kinetic energy = Gain in gravitational potential energy
`:. (1)/(2)mv^2 =- (GMm)/(2R) - (-(GMm)/(R )`
`:. v = sqrt((GM)/(R ) ...(ii)`
Comparing (i) & (ii) N = 2