Question

What is the recoil velocity of the gun of 8 kg when a bullet of mass 10 g is fired from it with a velocity of 400 m/s. please solve​

Answer 1

Answer:

$\rm = 0.5m \: {s}^{ - 1}$

Explanation:

Given,

• mass of a gun $\rm (m_1) = 8kg$
• mass of a bullet $\rm (m_2) = 0.01kg$

The bullet is fired with a velocity of 400m/s.

Find the recoil velocity of the gun.

Let's assume the recoil velocity as $\boldsymbol v \rm m \: s^{-1}$

Now,

We know that,

$\bullet \: \: \boldsymbol{ p = mv}$

Where,

• $\boldsymbol p$ denotes the momentum.
• $\boldsymbol m$ is the mass of the object.
• $\boldsymbol v$ is the velocity of the object.

Here, the gun is at rest so the initial velocity would be zero.

$\therefore \boldsymbol u = \rm 0m \: {s}^{ - 1}$

So, the total momenta of the gun and the bullet before firing,

$\rm = (m_1 + m_2) \ast \boldsymbol u$

$= (8 + 0.01) \ast 0$

$\rm = 0$

$\therefore \boldsymbol{p_1}\rm= 0kgm \: {s}^{ - 1}$

Total momenta of the gun and bullet after firing,

$= ({ \rm \: m_1} \ast v_1) + ({ \rm m_2} \ast \: v_2)$

$= (8 \times v) + (0.01 \times 400)$

$= 8v + 4$

$\therefore\boldsymbol{p_2} = 8v + 4 \rm \: kgm \: {s}^{ - 1}$

According to the law of conservation of momentum,

$\implies p_1 = p_2$

$\implies \: 0 = 8v + 4$

$\implies \: 8v = - 4$

$\implies \: v = \dfrac{ - 4}{8}$

$\therefore \: v = - 0.5$

∴ Recoil velocity of the gun is 0.5m/s

__________________________

Note: negative sign denotes the backward force of the recoiling.

Answer 2

QUESTION :-

What is the recoil velocity of the gun of 8 kg when a bullet of mass 10 g is fired from it with a velocity of 400 m/s

ANSWER :-

recoil velocity of the gun = 0.5 m/s

GIVEN :-

mass of the gun = 8 kg

mass of the bullet = 0.01 kg

velocity of the bullet = 400 m/s

TO FIND :-

recoil velocity of the gun = ?

SOLUTION :-

As no external force is acting on the

system, the total linear momentum of the system is conserved.

Conservation of linear momentum :-

Pi = Pf

Initial momentum Pi = 0

as the gun and the bullet do not move.

Final momentum = Pf = mg Vg + mb Vb

0=mg Vg + mb vb

⇒0=8Vg+(0.01) (400)

⇒|Vg|=0.5 m/s