Question

A bullet of mass 125gm leaves a rifle with a velocity of 500m/s . The rifle recoils with a velocity of 5m/s . The mass of the rifle.
E. 100 kg
F. 12.5 kg
G. 1.25 kg
H. 125 kg

Answer 1

Hint As we know the total momentum of the system is conserved if there is no external force acting on that. Gun recoil results from conservation of total momentum of the bullet-gun system: the backward recoil gun momentum balances the forward bullet momentum to maintain zero total momentum.

Complete step-by-step solution :
Conservation of momentum is actually a direct consequence of Newton's third law.
Momentum characterizes an object's opposition to change in motion. If this motion is in a straight line, we call it linear momentum; if motion is rotational we call it angular momentum. The basic idea is the quite same: moving things like to keep moving, and to change their motion we have to apply an external force. If no external force is present, then momentum doesn't change, i.e. it is conserved.
Now, A bullet coming out of a gun has a huge force on it. True enough, and that force is what moves the bullet forward. However, if you look at a bullet and gun together (while the bullet is still in the barrel but already heading out at full speed), you can say there is no net force on the bullet-gun system. So, the momentum of the bullet plus gun should be conserved.
Momentum can be given product of mass and its velocity:
$p = mv$
Conserving momentum as:
${m_1}{v_1} = {m_2}{v_2}$
Initially the momentum was zero therefore, final momentum will also be zero
$0 = {m_{bullet}}{v_{bullet}} + {m_{riffle}}{v_{riffle}}$
${m_{riffle}}{v_{riffle}} = - {m_{bullet}}{v_{bullet}}$
As velocity is a vector quantity, and the bullet is moving in a positive direction and riffle in the opposite direction therefore, we’ll take the rifle's velocity as negative.
${m_{riffle}} \times ( - 5) = - 125 \times 500$
${m_{riffle}} = 12.5kg$
Hence, option B is correct.

Note:- There are many conserved quantities in physics. Whenever there is dissipation of energy and if this dissipated energy can’t be calculated then we can’t calculate resultant energy of each body. Although the principle of conservation of energy is obeyed. In mechanics, these are the fundamental quantities which are conserved; energy, momentum and angular momentum. Mostly we use Conservation of momentum for describing collisions between objects.