Question

A bullet of mass 20g is fired from a gun with a muzzle velocity of 100
−1. Find therecoil of the gun if its mass is 5kg

Answer 1

Answer:

Given:

Mass of gun = 5 kg

Mass of bullet = 20 g

Velocity of bullet = 100 m/s

To find:

Recoil velocity of gun

Concept:

In the gun and bullet system, the initial and final velocity of gun and bullet is same and constant. since the gun and bullet is initially at rest , we can say that :

Final momentum of gun is equal and opposite to the final momentum of bullet.

Calculation:

$\bigstar \: \: \:P1 = - P2$

$= > (m1)(v1) = - (m2)(v2)$

$= > 5(v1) = - ( \dfrac{20}{1000} )(100)$

$= > v1 = - \dfrac{2}{5} = - 0.4 \: m {s}^{ - 1}$

So final answer is 0.4 m/s

Negative sign Indicates opposite direction of recoil velocity wrt movement of bullet.

Answer 2

SoluTion :-

✴ Given :-

• mass of bullet = 20g
• velocity of bullet = 100mps
• mass of gun = 5kg

✴ To Find :-

• Recoil velocity of gun

✴ Concept :-

✈ This question is completely based on concept of 'Conservation of momentum', because in this situation net force on the system is zero.

✴ Conversation :-

↪1000g = 1kg

↪ 20g = 0.02kg

✴ Calculation :-

$\mapsto\sf\:\red{initial\:momentum=final\:momentum}\\ \\ \mapsto\sf\:0 + 0 = P_g + P_b\\ \\ \mapsto\sf\:P_g= -P_b\\ \\ \mapsto\sf\:M_gV_g=-(M_bV_b)\\ \\ \mapsto\sf\:5\times V_g=-(0.02\times 100)\\ \\ \mapsto\sf\:V_b= -\dfrac{0.02\times 100}{5}\\ \\ \mapsto\:\boxed{\sf{\orange{V_g= -0.4\:mps}}}$

_________________________________

✒ Recoil velocity of gun = -0.4 mps

Note : Negative sign indicates opposite direction of recoil with respect to direction of movement of bullet.

✴ Additional information :

• Momentum is a scalar quantity.
• SI unit of momentum is kgm/s