A shell of mass `200g` is ejected from a gun of mass `4 kg` by an explosion that generate `1.05 kJ` of energy. The initial velocity of the shell is

Options

A. `80 " m "s^(-1)`
B. `40 " m "s^(-1)`
C. `120 " m"s^(-1)`
D. `100 " m "s^(-1)`

Answer

D

Explanation

Let recoil velocity of gun
`V= -(mv)/M `
Given , `m = 200 gm = 0.2 kg, M = 4 kg `
Due to conservative of energy
`1/2mv^(2) +1/2MV^(2)=1.05 xx10^(3)J `
`1/2mv^(2) +1/2M ((-mv)/M)^(2) = 1.05 xx10^(3)J `
`1/2 mv^(2) +1/2 (m^(2)v^(2))/M = 1.05 xx10^(3)J `
`v^(2) =10^(4) m//s `
Intial velocity of shell , v = 100 m/s