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From a rifle of mass $4 kg$ , a bullet of mass $50 g$ is fired with an initial velocity of $35 m / s .$ The initial recoil velocity of the rifle is [[1]] $m / s$ .

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Detailed Solution

The initial recoil velocity of the rifle is

7.8 m / s

.
Given
The mass of the gun

M = 4 kg

The mass of bullet,

m = 50 g

In SI unit, the mass of bullet,

m = 0.05 kg

Initial velocity of the bullet,

v = 35 m / s

Let the recoil velocity of the gun be

V m / s

.
Initially, before firing the bullet both gun and bullet were in rest so total momentum of gun and bullet is zero,
After firing,
Momentum of bullet

= mv,

Momentum of gun

= MV

Total momentum of bullet and gun after firing

= mv + MV

Since there is no external force applied on the system, so it can be considered that the total momentum after firing is equal to the total momentum before firing,

\Rightarrow mv + MV = 0

\Rightarrow MV = - mv

\Rightarrow V = - mv / M

On substituting the values, we get

\Rightarrow V = (0.05 \times 35) / 4

\Rightarrow V = - 0.44 m / s

Here, the negative sign shows that the recoil velocity of the gun is in the direction opposite to the velocity of the bullet.

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