Question

A bullet of mass 15 gram live the barrel of a gun with a velocity of 120 metre per second . the gun recoil with a velocity of 1 metre per second find the mass of the gun .​

Answer 1

Answer:

• Mass of the Gun (M) = 1.8 Kg.

Given:

1. Mass of the Bullet (m) = 15 grams = 0.015 Kg.
2. Velocity of bullet (u) = 120 m/s
3. Velocity of Gun (v) = 1 m/s

Explanation:

$\rule{300}{1.5}$

We Know, From  Law of Conservation of Momentum,

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

$\bold{Here}\begin{cases}\sf{P_i} \; \text{Denotes Initial Momentum} \\ \sf{P_f }\; \text{Denotes Final Momentum}\end{cases}$

But Before Firing The Initial Momentum is Zero.

Substituting.

$\large{\tt \hookrightarrow P_f = 0}$

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

Substituting the values

$\large{\tt \hookrightarrow 0.015 \times 120 + M \times (1) = 0 }$

$\large{\tt \hookrightarrow 0.015 \times 120 + M \times (-1) = 0}$

As The Recoil velocity of Gun is in Opposite Direction to the velocity of Bullet.

$\large{\tt \hookrightarrow 0.015 \times 120 + ( - M) = 0}$

$\large{\tt \hookrightarrow 0.015 \times 120 = M}$

$\large{\tt \hookrightarrow M = 0.015 \times 120 }$

$\large{\tt \hookrightarrow M = 0.15 \times 12 }$

$\huge{\boxed{\boxed{\tt M = 1.8 \; Kg}}}$

∴ Mass of The Gun is 1.8 Kg.

$\rule{300}{1.5}$

Answer 2

Answer:

We have equation :

m₁ v₁ = m₂ v₂

Here :

m₁ = 15 g or 0.015 kg

v₁ = 120 m / sec

m₂ = ?

v₂ = 1 m / sec

0.015 × 120 = 1 × m₂

m₂ = 1.8 kg.

Therefore , mass of the gun is 1.8 kg.