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: Understanding the Concept:
Tangential acceleration \(a_t = r\alpha\). Centripetal acceleration \(a_c = \frac{v^2}{r}\).

Step 2: Apply the condition:
Given \(a_c = \frac13a_t\):
\[ \frac{v^2}{r} = \frac{r\alpha}{3} \Rightarrow v^2 = \frac{r^2\alpha}{3} \]

Step 3: Take the root:
\[ v = r\sqrt{\frac\alpha3} \]
Option (A), \(\frac{r\alpha}{3}\), is an acceleration, not a speed. Options (B) and (D) put r inside the root, which does not give the units of speed when \(\alpha\) is in rad/s\(^2\).

Final Answer:
The speed is \(v = r\sqrt{\frac\alpha3}\), option (C). \[ \boxed{v = r\sqrt{\frac{\alpha}{3}}} \]