Question

A machine gun fires bullets of mass $30\text{ g}$ with velocity of $1000\text{ m/s}$. The man holding the gun can exert a maximum force of $300\text{ N}$ on it. How many bullets can he fire per second at most?

• A. 3
• B. 6
• C. 10
• D. 9

Hint:

Force is the rate of change of momentum. For $n$ objects per second, use $F = n \cdot m \cdot v$.

Answer 1

The Correct Option is A

textbf{Step 1:} Calculate the momentum ($p$) of a single bullet using the formula: \[ p = m \cdot v \] textbf{Step 2:} Convert mass from grams to kilograms and substitute values ($m = 0.03\text{ kg}$, $v = 1000\text{ m/s}$): \[ p = 0.03 \cdot 1000 = 30\text{ kg}\cdot\text{m/s} \] textbf{Step 3:} Use Newton's second law in terms of momentum. The force $F$ exerted by firing $n$ bullets per second is: \[ F = n \cdot \frac{\Delta p}{\Delta t} \] textbf{Step 4:} Since $n$ is the number of bullets per second, $\Delta t = 1\text{ s}$ and $\Delta p = 30\text{ kg}\cdot\text{m/s}$ per bullet. Given $F_{\text{max = 300\text{ N}$: \[ 300 = n \cdot 30 \] textbf{Step 5:} Solve for $n$: \[ n = \frac{300}{30} = 10 \text{ bullets/s} \]