Question

A cannon of mass 1000 kg can fire a bolt of 20 kg with a muzzle velocity of $300\frac{m}{s}$. If the cannon is free to move, the backwards velocity of the cannon after the bolt is fired will be:

• A. 10 g mass
• B. 20 g mass
• C. 15 g mass
• D. 25 g mass

Answer 1

The correct option is A

10 g mass

Let the velocity of the cannon after firing the bolt be $-v$. Minus sign indicates that the cannon will move backwards.
Muzzle velocity is the velocity of a bolt with respect to the cannon.
So, the velocity of the bolt with respect to ground will be $300-v$.
From the law of conservation of momentum, the total momentum of the cannon and the bolt before firing should be equal to the total momentum of cannon and bolt after firing.
$Hence,0=1000\times (-v)$
$+20\times (300-v)$
(total initial momentum is 0 as both bodies were at rest before firing)
$\Rightarrow 0=-1000v+6000-20v$
$\Rightarrow 1020v=6000$
$\Rightarrow v=5.9\frac{m}{s}$
Hence, the backward velocity of cannon will be almost $5.9\frac{m}{s}$.