Question 78: Centre of Mass and Rotational Motion

Question

An average force of $125 \mathrm{~N}$ is applied on a machine gun firing bullets each of mass $10 \mathrm{~g}$ at the speed of $250 \mathrm{~m} / \mathrm{s}$ to keep it in position. The number of bullets fired per second by the machine gun is :

Accepted Answer

To find the number of bullets fired per second, we can use the concept of momentum. When the machine gun fires bullets, it experiences a backward force due to the conservation of momentum. The force applied on the machine gun is used to balance this backward force.
First, let's find the momentum of each bullet:
Momentum = Mass ÃÂ Velocity
Bullet mass = $10 \mathrm{~g} = 0.01 \mathrm{~kg}$
Bullet velocity = $250 \mathrm{~m/s}$
Momentum per bullet = $0.01 \mathrm{~kg} \cdot 250 \mathrm{~m/s} = 2.5 \mathrm{~kg \cdot m/s}$
Now let's find the momentum per second that needs to be balanced by the applied force:
Force = $125 \mathrm{~N}$
Momentum per second = Force ÃÂ Time
Since we are considering a time interval of 1 second, the momentum per second is equal to the applied force:
Momentum per second = $125 \mathrm{~N}$
Now, let's find the number of bullets fired per second:
Number of bullets = Momentum per second / Momentum per bullet
Number of bullets = $\frac{125 \mathrm{~N}}{2.5 \mathrm{~kg \cdot m/s}}$
Number of bullets = 50
Therefore, the machine gun fires 50 bullets per second.

Answer

25

Answer

50

Answer

5

Answer

100

Centre of Mass and Rotational Motion

An average force of 125 \mathrm{~N} is applied on a machine gun firing bullets each of mass 10 \mathrm{~g} at the speed of 250 \mathrm{~m} / \mathrm{s} to keep it in position. The number of bullets fired per second by the machine gun is :

Choose the correct answer: