A shell of mass 20 g is fired by a gun of mass 10 kg. If the shell leaves the gun with a speed of `80 m s^(-1)~ , the speed of recoil of the gun is

Options

A. `32 cm s^(-1)`
B. `16 cm s^(-1)`
C. `10 cm s^(-1)`
D. `24 cm s^(-1)`

Answer

B

Explanation

Here, mass of the shell, `m = 20 g = 20 xx 10^(-3)` kg = 0.02 kg
Mass of the gun, M = 10 kg
Speed of the shell, `v = 80 ms^(-1)`
Let V be speed of recoil of the gun.
According to law of conservation of linear momentum, 0 = my + MV
`V =- (mv)/(M) = (0.02 kg xx 80 ms^(-1))/(10kg) = -1.6 xx 10^(-1) ms^(-1)`
` =-16 cms^(-1)`
where, -ve sign shows that gun moves backward as the shell moves forward i.e., the gun recoils.