A cannon of mass 1000 kg can fire a bolt of 20 kg with a muzzle velocity of 300 m/s. If the cannon is free to move, the backward velocity of cannon after the bolt is fired is:
A cannon of mass 1000 kg can fire a bolt of 20 kg with a muzzle velocity of 300 m/s. If the cannon is free to move, the backward velocity of cannon after the bolt is fired is:
The correct option is A 10 g mass
Let the velocity of the cannon after firing the bolt be −v. Here, minus sign indicates that the cannon moves backward.
Muzzle velocity is the velocity of a bolt with respect to the cannon.
So, the velocity of the bolt with respect to ground is 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×(−v)+20×(300−v)
(total initial momentum is 0 as both bodies were at rest before firing)
⇒0=−1000v+6000−20v
⇒1020v=6000
⇒v=5.9m/s
Hence, the backward velocity of cannon is 5.9 m/s.
10 g mass
Let the velocity of the cannon after firing the bolt be −v. Here, minus sign indicates that the cannon moves backward.
Muzzle velocity is the velocity of a bolt with respect to the cannon.
So, the velocity of the bolt with respect to ground is 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×(−v)+20×(300−v)
(total initial momentum is 0 as both bodies were at rest before firing)
⇒0=−1000v+6000−20v
⇒1020v=6000
⇒v=5.9m/s
Hence, the backward velocity of cannon is 5.9 m/s.
