Question

A riffle of mass $25\text{kg}$ fires at the rate of 6 bullets per second. If the mass of each bullet is $30\text{g}$ and the velocity of the bullet when it leaves the gun is $1080\text{km/h}$, find the magnitude of average force required to hold the gun while firing (neglect recoil speed of riffle).

• A. $40\text{N}$
• B. $45\text{N}$
• C. $54\text{N}$
• D. $60\text{N}$

Answer 1

The correct option is C $54\text{N}$

We know
Rate of change of momentum of the bullet in forward firection
= Force required to hold the gun.
$\therefore |F_{avg}|=\frac{|\Delta p|}{\Delta t}$
$\Delta p\text{for one bullet in 1 s is}m(v_f-v_i)=mv$
$\Delta p\text{for 6 bullet in 1 s is}6m(v_f-v_i)=6mv$
$\Rightarrow |F_{avg}|=\frac{|\Delta p|}{\Delta t}=\frac{6mv}{1}\text{N}$
$=\frac{6\times 30\times {10}^{-3}\times (1080\times \frac{5}{18})}{1}=54\text{N}$