Question

A person of mass 50 kg is standing on ice and fires a bullet of 100 gm with a velocity of 600 m/sec by a gun of 10 kg. What will be the recoil velocity of the person?
1. 3 m/sec
2. 2 m/sec
3. 1 m/sec
4. 0 m/sec

Answer 1

Correct Answer - Option 3 : 1 m/sec

CONCEPT:

Linear momentum

• It is defined as the product of the mass of an object, m, and its velocity, v. It, is a vector quantity.​

​⇒ P = mv

Conservation of momentum

• If the force applied to the system of particles is zero, then the total momentum of the system of particles will remain conserved.

\(⇒ P_{1}+P_{2}+P_{3}+...+P_{n}=constant\)

CALCULATION:

Given - mass of the person (m_P) = 50 kg, mass of bullet (m_B) = 100 gm = 0.1 kg, mass of bullet (mG) = 10 kg, and final velocity of bullet (v_B) = 600 m/sec

Initially the person, gun, and the bullet all are at rest, so the initial momentum of the system is given as,

⇒ P_I = 0     -----(1)

• After firing a bullet let the recoil velocity of the gun and the person be v.
• So the final momentum of the system is given as,

⇒ P_F = P_P + P_G + P_B

Where PP = final momentum of person, PG = final momentum of the gun, and PB = final momentum of the bullet

⇒ PF = m_Pv + m_Gv + m_Bv_B

⇒ PF = 50v + 10v + 0.1 × 600

⇒ PF = 60v + 60     -----(2)

According to the conservation of momentum, the final momentum should be equal to the initial momentum.

⇒ P_F = P_I

⇒ 60v + 60 = 0

⇒ 60v = -60

⇒ v = -1 m/sec

• Hence, option 3 is correct.