Question

A machine gun having a power 27 kw fires 'n' bullets per second each of mass 10 gm. If the
velocity of each bullet is 300 ms -1, the value of 'n' is
60
120
600
300​

Answer 1

Given :

• Power of machine Gun, P = 27 kW = 27 × 1000 w = 27,000 w
• n number of bullets are fired per second so time , t = 1 s
• Velocity of each bullet, v = 300 ms⁻¹
• Mass of each bullet, m = 10 gm = 10/1000  kg = 0.01 kg

To find :

Value of 'n' = ?

Knowledge required :

• Formula to calculate Kinetic energy

$\red{\bigstar}\boxed{\sf{K.E.=\dfrac{1}{2}\;m\;v^2}}$

• Relation between Power and Kinetic Energy

$\red{\bigstar}\boxed{\sf{P=\dfrac{K.E.}{t}}}$

[ Where K.E. is the kinetic energy of a body, mass is m , velocity is v , P is power and t is time ]

Solution :

Calculating K.E. of 'n' bullets

$\implies\sf{K.E.\:of\:'n'\:bullets=n\times\dfrac{1}{2}\;m\;v^2}$

$\implies\sf{K.E.\:of\:'n'\:bullets=n\times\dfrac{1}{2}\times(0.01)\times(300)^2}$

$\implies\underline{\underline{\red{\sf{K.E.\:of\:'n'\:bullets=450\;n\;\;Joules}}}}$

Calculating value of 'n'

$\implies\sf{P=\dfrac{K.E.\:of\:n\:bullets}{t}}$

$\implies\sf{27,000=\dfrac{450\;n}{1}}$

$\implies\sf{n=\dfrac{27,000}{450}}$

$\implies\underline{\underline{\large{\red{\sf{\;n=60\;}}}}}$

Therefore,

• Number of bullets is equal to 60 .

Option (1) 60 is correct.

Answer 2

Answer:

a) 60

Explanation:

Given that, a machine gun having a power 27 kw fires 'n' bullets per second each of mass 10 gm. If the velocity of each bullet is 300 m/s.

We have to find the value of n.

Potential energy is 27 kW or 27000 W (1kW = 1000W), mass is 10 gm or 0.01 kg, time is 1 sec and velocity is 300 m/s.

Energy which a body possesses by virtue of being in motion is known as Kinetic energy.

Kinetic energy = 1/2 mv²

Substitute the values,

→ K.E. = 1/2 × 0.01 × (300)²

→ K.E. = 0.01/2 × 90000

→ K.E. = 450 J

Power = 27000 W

We know that, the relation between Kinetic energy, power and time is:

Power = Kinetic energy/Time

And as per given condition we have to find the 'n' number of bullets.

Power = n × Kinetic energy/Time

Substitute the values,

→ 27000 = n × 450 /1

→ 27000/450 = n

→ 60 = n

Hence, the value of n is 60.