Question

A bullet of mass 50gm is fixed by a gun of 5kg .If velocity of bullet is 100m/s then find the recoil velocity of gun

Answer 1

Answer :

Mass of bullet = 50g = 0.05kg

Mass of gun = 5kg

Velocity of bullet = 100m/s

We have to find recoil velocity of gun$.$

◈ Recoil velocity of gun :

Here, No net force act on the system (Gun + Bullet) we can solve this question by applying concept of momentum conservation.

Recoil velocity, V = -mv/M

• M is the mass of the gun
• m is the mass of bullet
• v is the velocity of bullet

➝ V = -mv/M

➝ V = -(0.05 × 100)/5

➝ V = -5/5

➝ V = -1m/s

[፨ Negative sign shows opposite direction.]

◈ Formula Derivation :D

Initial momentum of whole system will be zero. (i.e., both are at rest)

As per law of momentum conservation, Initial momentum of whole system will be equal to the final momentum of whole system.

⇒ Pi = Pf

⇒ 0 = mv + MV

⇒ MV = -mv

⇒ V = -mv/M ^^"

☃ God_Bless :)

Answer 2

Answer

Recoil velocity of gun = -1 m/s

Given

A bullet of mass 50 gm is fixed by a gun of 5 kg . Velocity of bullet is 100 m/s

To Find

Recoil velocity of gun

Concept Used

We need to apply conservation of momentum ,

$\to\ \rm{\pink{Initial\ momentum=Final\ momentum}}\\\\\to\ \rm{\green{P_i=P_v}}\\\\\to\ \rm{\blue{m_iv_i=m_vv_v}}$

Solution

$\rm Mass\ of\ bullet,m_b=50\ g=0.05\ kg\\\\\rm Mass\ of\ gun,m_g=5\ kg\\\\\rm Velocity\ of\ bullet,v_b=100\ m/s\\\\\rm Recoil\ velocity\ of\ gun\ ,v_g=?\ m/s\\\\\rm Apply\ conservation\ of\ momentum,\\\\\rm \to\ P_i=P_v\\\\\to\ \rm (m_g+m_b)v_i=m_gv_g+m_bv_b\\\\\to\ \rm (m_g+m_b)(0)=m_gv_g+m_bv_b\\\\\rm Since,both\ gun\ and\ bullet\ are\ in\ rest.So,Initial \\\\\rm velocity\ is\ zero\ (0)\\\\\rm \to\ 0=(5)v_g+(0.05)(100)\\\\\rm \to\ 5v_g=-(0.05)(100)$

$\to\ \rm 5v_g=-\dfrac{5}{100}\times 100\\\\\to\ \rm 5v_g=-\dfrac{5}{\cancel{100}}\times \cancel{100}\\\\\to\ \rm 5v_g=-5\\\\\to\ \rm{\pink{v_g=-1\ m/s\ \; \bigstar}}$

Note : Negative sign of velocity denotes motion of recoil in opposite direction