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=20 g = 20 \times 10^{-3} \, kg = 0.02 kg $
Mass of the gun, $M = 100\: kg$
Speed of the shell, $v = 80\, m \, s^{-1}$ Let V be speed of recoil of the gun.
According to law of conservation of linear momentum,
$0= mv + M V$
$V = - \frac{mv}{M}$
$= - \frac{0.02 kg\times80 m s^{-1}}{100 kg} = - 1.6\times 10^{-2} m s^{-1}$
$ = - 1.6 cm s^{-1}$
-ve sign shows that gun moves backward as the shell moves forward i.e. the gun recoils.