Question

A machine gun fires 240 bullets per minute with a certain velocity. If
the mass of each bullet is 10 gm and the power of the gun is 7.2 kW, the
velocity with which each bullet is fired must be​

Answer 1

Answer:

pls see the attachment

Answer 2

Answer:

A machine gun fires 240 bullets per minute with a certain velocity. If

the mass of each bullet is 10 gm and the power of the gun is 7.2 kW, the

velocity with which each bullet is fired must be​ $600\ m/s$

Explanation:

Power of the gun can be expressed as,

Power (P)  $= \frac{Work\\ done\ (W)}{time\ (t)}$  ...(1)

Work done by the bullet will be equal to the change in kinetic energy which can be written as,

$K.E = \frac{1}{2} m v^{2}$  

where m - The mass of the bullet  and

           v - velocity

Let n be the number of bullets,

then power becomes,

$\text { Power }=n \times \frac{\frac{1}{2} m v^{2}}{t}$

Or

$P= \frac{n}{t} \times \frac{1}{2} m v^{2}$    ...(3)

By rearranging the above equation, we can obtain the formula for velocity.

$v^{2} = \frac{2P}{m} \times\frac{t}{n}$

$v = \sqrt{ \frac{2P}{m} \times\frac{t}{n}}$      ...(4)

In the question, it is given that,

$m = 10\ g = 0.01\ kg$

$\frac{t}{n} = \frac{minute}{240\ bullets}$

   $=\frac{ 60\ s}{240} = \frac{1s}{4}$  

$P = 7.2\ KW = 7.2\times10^{3}\ Watt$

Substitute these values into equation (4)

We get,

$v = \sqrt{\frac{2\times7.2\times10^{3} }{0.01} \times\frac{1}{4}}$

   $= \sqrt{360000}$

    $= 600\ m/s$

     

• The velocity of the bullet =  $600\ m/s$