Question

A machine gun fires 60bullets per minute with a velocity of 700m/s.if each bullet has a mass of 50gm.find the power developed by the gun

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

Mass of bullet (m) = 50 grams = 0.05 Kg.

Number of bullets per minute (n) = 60 bullets per sec.

Velocity of bullet (v) = 700 m/s.

$\huge{\bold{\underline{Explanation:-}}}$

Kinetic energy,

$\large{\bold{K.E = \frac{1}{2}mv^2}}$

Substituting the values,

$\large{K.E = \frac{1}{2} \times 0.05 \times (700)^2}$

$\large{K.E = \frac{1}{2} \times 0.05 \times 490000}$

$\large{K.E = \frac{1}{ \cancel{2}} \times 0.05 \times \cancel{490000}}$

$\large{K.E = 0.05 \times 245000}$

$\large{\boxed{K.E = 12,250 \: J}}$

Kinetic energy of 1 bullet = 12,250 J.

Kinetic energy of 60 bullet = 12,250 × 60

Kinetic energy of 60 bullets = 7,35,000 J.

Power is rate of doing work

Therefore,

$\large{\bold{Power = \frac{Work \: done}{Time \: taken}}}$

Substituting the values,

$\large{P = \frac{7,35,000}{1 \: minute}}$

As we know 1 minute = 60 seconds.

$\large{P = \frac{7,35,000}{60 \: seconds}}$

$\large{P = \frac{7,35,000}{60}}$

$\large{P = \frac{ \cancel{7,35,000}}{ \cancel{60}}}$

$\large{P = 12,250 \: W}$

$\huge{\boxed{\boxed{P = 12.250 \: KW}}}$

So, the power developed by the gun is 12.250 Kilo Watts.