Question

A bullet of mass 10 gram is fired from a rifle with a speed of 3600km/h calculate the speed of the recoil of the rifle ,if its mass is 5kg

Answer 1

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

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

• Mass of the bullet (m) = 10 grams,
• Speed of bullet (u) = 3600 Km/h,
• Mass of the gun(M) = 5 Kg.
• Speed of the gun = v.

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

$\rule{300}{1.5}$

Firstly Converting the units in too S.I system,

10grams = ? Kg,

$\large{\tt m = 1 \: gram = 0.001 \: kg}$

Therefore,

$\large{\tt \leadsto m = 10 \: grams = 10 \times 0.001 \: kg}$

This implies,

$\large{\boxed{\tt m = 0.01 \: kg}}$

3600 Km/h = ? m/s.

$\large{\tt u = 1 \: Km/h = \dfrac{5}{18} \: m/s}$

$\large{\tt \leadsto u = 3600 \: Km/h = 3600 \times \dfrac{5}{18} \: m/s}$

$\large{\tt \leadsto u = 3600 \: Km/h = \cancel{3600} \times \dfrac{5}{\cancel{18}} \: m/s}$

This implies,

$\large{\boxed{\tt u = 1000 \: m/s}}$

$\rule{300}{1.5}$

$\rule{300}{1.5}$

From Law of Conservation of momentum

Statement:-

The momentum of body remains constant unless and until a net External Force is applied on it.

Now,

$\large{\boxed{\tt P_i = P_f}}$

Here,

• ${\tt P_i}$ = Initial momentum,
• ${\tt P_f}$ = Final momentum.

Here the whole system is at rest initially,

Therefore Initial momentum of the system will be Zero,

Therefore,

$\large{\tt \leadsto 0 = Mv + mu}$

Substituting the values,

$\large{\tt \leadsto 0 = 5 \times v + 0.01 \times 1000}$

$\large{\tt \leadsto 0 = 5 \times v + \dfrac{1}{100} \times 1000}$

$\large{\tt \leadsto 0 = 5 \times v + \dfrac{1}{\cancel{100}} \times \cancel{1000}}$

$\large{\tt \leadsto 0 = 5v + 10}$

$\large{\tt \leadsto 5v = - 10}$

$\large{\tt \leadsto v = \dfrac{-10}{5}}$

$\large{\tt \leadsto v = \dfrac{\cancel{-10}}{\cancel{5}}}$

$\huge{\boxed{\boxed{\tt v = - 2 \: m/s}}}$

So, The Recoil velocity of the Gun is - 2 m/s.

Note:-

• Here the Negative Sign indicates that the Gun is moving in opposite direction that of the bullet.

$\rule{300}{1.5}$

Answer 2

Answer:

I hope it helps you

And any doubt then ask