Question

The machine gun fires 240 bullets per minute. If the mass of each bullet is 10 g and the velocity of the
bullets is 600 ms1, then the power (in kW) of the gun is
(1) 43200 (2) 432 (3) 72 (4) 7.2

Answer 1

Given that, the machine gun fires 24/ bullets per minute. Mass of each bullet is 10 g and the velocity of the bullets is 600 m/s.

We have to find the power of the gun in kW.

Power is defined as work done upon time.

P = W/t ............ (1st equation)

Here, work is done in the form of Kinetic energy. And kinetic energy is 1/2 mv²

W = K.E. = 1/2 mv² .......(2nd equation)

From (1st equation) and (2nd equation) we can say that,

P = (1/2 mv²)/t

And from above data we have, mass (m) = 10 g = 10 × 10-³ kg, velocity (v) = 600 m/s, time = 1 min = 60 sec and number of bullets (n) = 240

Substitute the values,

P = (1/2 × 10 × 600 × 600)/(60 × 1000)

P = (360000 × 10-³)/12

P = 30000 × 10-³

For 240 (n) bullets:

P = n × 5000

P = 240 × 30000 × 10-³

P = 7200000 × 10-³

P = 7200 W

P = 7.2 kW

Option d) 7.2 kW

Answer 2

GIVEN:

• Gun fires 240 bullets per minute
• Mass of each bullet = 10g
• Velocity of bullets = 600 m/s

TO FIND:

• Power of gun in kW

SOLUTION:

Using the formula

P = W/t

Where

• P : power
• W : work
• t : time

Substituting W = ½ mv²

→ P = (½mv²)/t

Mass = 10g = 10-²kg

Time = 1min = 60s

Velocity = 600m/s

Substituting the values we have

→ P = [½ × 10 × ( 600 )²]/60 × 10³

→ P = ( 360000 × 10-³ )/12

→ P = 30000 × 10-³

For 240 bullets

→ P= n × 5000

→ P = 240 x 30000 × 10-³

→ P = 7200000 x 10-³

→ P = 7200 W

→ P = 7.2 kW {Answer[option( d )]}