A shell of mass 200g is fired by a gun of mass 100kg. If the muzzle speed of the shell is `80ms^(-1)` , then the rcoil speed of the gun is

Options

A. `16"cms"^(-1)`
B. `8"cms"^(-1)`
C. `8"ms"^(-1)`
D. `16"ms"^(-1)`

Answer

A

Explanation

Here,
Mass of shell, `m=200g=200xx10^(-3)kg`
Mass of the gun, M=100kg
Muzzle speed of the shell, `V=80ms^(-1)`
Recoil spped of the gun, v=?
According to the principle of conservation of linear momentum,
mV+Mv=0
`v=-(mV)/(M)=-((200xx10^(-3)kg)(80 ms^(-1)))/(100kg)`
`=16xx10^(-2)ms^(-1)=-15cm s^(-1)`
-ve sign shows that the recoil speed of the gun will be in a direction opposite to that of the shell.