A gun fires a small bullet with kinetic energy K. Then kinetic energy of the gun while recoiling is

Options

A. K
B. more than K
C. less than K
D. `sqrt(K)`

Answer

C

Explanation

Recoil velocity of the gun, `v = -(mu)/(M)` …(i)
-ve sign shows that recoil of the gun
Where m is the mass of the bullet, M is the mass of the gun and u is the velocity of bullet.
`:.` Kinetic energy of the bullet, `K = (1)/(2) mu^(2)`
Kinetic energy of the gun while recoilling,
`K' = (1)/(2) mv^(2)`
`:.` `(K')/(K) = (M)/(m) ((v^(2))/(u^(2))) = (M)/(m) ((m)/(M))^(2) = (m)/(M)` (Using (i))
As m lt lt M `:.` K' lt K