A machine gun fires a bullet of mass 65g with a velocity of 1300m/s. The man holding it can exert a maximum force of 169N on the gun. The number of bullets he can fire per second will be

• A) 1
• B) 2
• C) 3
• D) 4

To determine how many bullets the man can fire per second, we first need to calculate the momentum of each bullet and the maximum momentum the man can handle based on the force he can exert.

Calculating Bullet Momentum

The momentum (p) of a bullet can be calculated using the formula:

p = mass × velocity

Given that the mass of the bullet is 65 grams (which is 0.065 kg) and the velocity is 1300 m/s, we can find the momentum:

p = 0.065 kg × 1300 m/s = 84.5 kg·m/s

Understanding Force and Time

The force exerted by the man can be related to the change in momentum over time using the formula:

Force = Change in momentum / Time

Rearranging this gives us:

Time = Change in momentum / Force

Calculating Maximum Bullets Fired

To find out how many bullets can be fired per second, we need to determine how much momentum the man can handle in one second:

Maximum momentum per second = Force × Time

Assuming the time is 1 second, we have:

Maximum momentum = 169 N × 1 s = 169 kg·m/s

Finding the Number of Bullets

Now, we can find the number of bullets fired per second by dividing the maximum momentum by the momentum of one bullet:

Number of bullets = Maximum momentum / Momentum of one bullet

Number of bullets = 169 kg·m/s / 84.5 kg·m/s ≈ 2

Final Answer

The man can fire approximately 2 bullets per second. Therefore, the correct option is B) 2.