Question

A shell of mass 20 g is fired by a gun of mass 100 kg. If the shell leaves the gun with a speed of 80 m $s^{-1}$. the speed of recoil of the gun is

• A. 3.2 cm $s^{-1}$
• B. 1.6 cm $s^{-1}$
• C. 1 cm $s^{-1}$
• D. 2.4 cm $s^{-1}$

Answer 1

Answer: (B)

Here,
Mass of the shell,$m=20g=20\times 10^{-3}kg=0.02kg$
Mass of the gun, $M=100kg$
Speed of the shell, $v=80m{s}^{-1}$ Let V be speed of recoil of the gun.
According to law of conservation of linear momentum,
$0=mv+MV$
$V=-\frac{mv}{M}$
$=-\frac{0.02kg\times 80m{s}^{-1}}{100kg}=-1.6\times 10^{-2}m{s}^{-1}$
$=-1.6cm{s}^{-1}$
-ve sign shows that gun moves backward as the shell moves forward i.e. the gun recoils.