Question

A bullet is fired by a light rifle and the other with a heavy rifle by the same force. Which rifle will cause more injury to the shoulder

• A. light rifle
• B. heavy rifle
• C. both cause the same injury
• D. information is insufficient

Answer 1

The correct option is A

light rifle

Step 1. Given data

Two identical bullets are fired with the same force. One bullet is fired with the light rifle and one bullet is fired by the heavy rifle.

Step 2. Explanation for the correct option

1. Momentum is how we measure the mass that is in motion. Any moving object will have momentum.
2. Momentum is equal to the product of the mass and the velocity.
3. The momentum of the bullet depends on the backward momentum of the rifle.
4. As per Newton's law of motion, the recoil velocity is equal to the bullet's velocity, making it lighter.
5. For heavy rifles, the recoil velocity is small, and for the light rifle, the recoil velocity is large due to the law of conservation of momentum so the light rifle will hurt more in the shoulder.

Let $m_1$ be the mass of light gun and $v_1$ be the velocity of light gun

$m_2$ be the mass of heavy gun and $v_2$ be the velocity of heavy gun

Since, $m_2$ is greater than $m_1$

For $m_1{v}_1=m_2{v}_2$

When $m_2$ is greater, $v_2$ will be less then $v_1$

Thus, light rifle will hurt more to the shoulder.

Hence, the correct option is $\left(A\right)$.