Question

Q1.A machine gun fires 200 bullets per minute with a velocity of 60 m/s. What is the
power of the machine gun, given that the mass of each bullet is 0.05 g?​

Answer 1

• Power: Power is the amount of energy transferred or converted

The unit of power is watt or J/s • Its dimensional formula is: [M L² T-³].

Calculation:

Given: v= 700 m/s, m = 50 g = 0.05 kg, n/t = 60 bullets/min 1 bullet/s

The power developed by the gun is given by formula -

Power = Work done / time

Power = n x mv² t

Power = x/mv² n

Power = 1 x × 0.05 × 700²

Power = 12250 watt

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Answer 2

Step-by-step explanation:

Given:

A machine gun fires 200 bullets per minute with a velocity of 60 m/s.

Mass of each bullet is 0.05 kg

(Unit of mass of the bullet should be kg in the question.)

To Find :

• Power of the machine gun.

Solution :

❖ We know that power is measured as the rate of work done per unit time.

It is a scalar quantity having only magnitude.

SI unit : W

First of all we have to find work done or better to say kinetic energy of bullets.

Kinetic energy of n bullets is given by

➠ K = n × 1/2 mv²

➠ K = 200 × 1/2 (0.05) (60)²

➠ K = 100 × 0.05 × 3600

➠ K = 5 × 3600

➠ K = 18,000 J

♦ Power of the machine gun :

$\sf:\implies\ Power=\dfrac{Energy}{Time}$

Time = 1 min = 60 s

$\sf:\implies\:P=\dfrac{18000}{60}$

$:\implies\:\underline{\boxed{\bf{\orange{P=300\:W}}}}$