Question

A machine gun fires a bullet of mass 40g with a speed of \(600\text{ ms}^{-1}\). The person holding the gun can bare maximum force of 168N on it. The number of bullets that can be fired from the gun per second is

• A. \(8\)
• B. \(7\)
• C. \(6\)
• D. \(5\)

Hint:

Tangential acceleration is r times alpha and centripetal acceleration is v squared over r.

Answer 1

The Correct Option is B

Step 1: Use kinematics too:
Starting from rest, $\omega = \alpha t$ and $v = r\alpha t$, so $a_c = \frac{v^2}{r} = r\alpha^2t^2$.

Step 2: Condition:
$r\alpha^2t^2 = \frac{r\alpha}{3}$ gives $t^2 = \frac{1}{3\alpha}$. So $v = r\alpha t = r\alpha\sqrt{\frac{1}{3\alpha}} = r\sqrt{\frac\alpha3}$ (C).

Final Answer:
$r\sqrt{\alpha/3}$. \[ \boxed{v = r\sqrt{\frac{\alpha}{3}}} \]