Question

from a rifle of mass 4 kg ,a bullet of mass 50 g is fired with an initial velocity of 35 m/s calculate the initial recoil velocity of the rifle ​

Answer 1

${ \huge \bf { \mid{ \overline{ \underline{Question}}} \mid}}$

From a rifle of mass 4 kg ,a bullet of mass 50 g is fired with an initial velocity of 35 m/s calculate the initial recoil velocity of the rifle ?

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

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

• Mass of Bullet (m) = 50 grams.
• Velocity of the Bullet after Firing (u) = 35m/s.
• Mass of The Rifle (M) = 4 kg.
• Let the recoil velocity of the Pistol be "v".

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

$\rule{300}{1.5}$

From Law of Conservation of momentum,

Initial Momentum = Final Momentum.

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

But Before Firing,

The whole system(Gun & Bullet) is at Rest.

Therefore, Initial momentum will be zero. Then the equation becomes,

$\large{\leadsto {\underline{\underline{\tt P_f = 0}}}}$

Now,

Formulating the Values of Final Momentum.

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

• M = Mass of Rifle.
• m = Mass of Bullet.
• u = Velocity of bullet.
• v = Velocity of Rifle.

Substituting the values,

$\large{\tt \leadsto 50 \times 10^{-3} \times 35 + 4 \times v = 0}$

(Mass of bullet (m) is 50 grams = 50 × 10⁻³ Kg.)

Simplifying,

$\large{\tt \leadsto 1750 \times 10^{-3} + 4v = 0}$

$\large{\tt \leadsto 1.750 + 4v = 0}$

$\large{\tt \leadsto 4v = - 1.750}$

$\large{\tt \leadsto v = \dfrac{- 1.750}{4}}$

$\large{\tt \leadsto v = - 0.4375}$

Approximately it Equals,

$\huge{\boxed{\boxed{\tt v = - 0.44 \: m/s}}}$

So, the Initial Recoil velocity of Rifle is 0.44 m/s

Note:-

• Here The negative sign of recoil velocity is because it is moving opposite to the Motion of the Bullet .

$\rule{300}{1.5}$

Answer 2

$\bold{\large{\underline{\underline{\sf{StEp\:by\:stEp\:explanation:}}}}}$

From Law of Conservation of momentum »

Law of conservation of momentum is defined as a principle in physics that says that some parts in an isolated system remaining steady and unchanging over time even when others are moving.

Initial Momentum = Final Momentum.

$\huge{\boxed{\sf P_i = P_f}}$

But Before Firing,

The whole system(Gun & Bullet) is at Rest.

Therefore, Initial momentum will be zero. Then the equation becomes,

$\sf{ P_f = 0}$

Now,

Formulating the Values of Final Momentum.

$\sf{mu + Mv = 0}$

• M = Mass of Rifle.
• m = Mass of Bullet.
• u = Velocity of bullet.
• v = Velocity of Rifle.

Substituting the values,

$\sf {50 \times 10^{-3} \times 35 + 4 \times v = 0}$

(Mass of bullet (m) is 50 grams = 50 × 10⁻³ Kg.)

Simplifying,

$\sf{ 1750 \times 10^{-3} + 4v = 0}$

$\sf{ 1.750 + 4v = 0}$

$\sf{4v = - 1.750}$

$\sf {v = \dfrac{- 1.750}{4}}$

$\sf {v = - 0.4375}$

$\green{\sf v = - 0.44 \: m/s \:apx.}$

Hence, the Initial Recoil velocity of Rifle is 0.44 m/s