Question

A body of mass 1 kg strikes elastically with another body at rest and continues to move in the same direction with one fourth of the initial velocity. What will be the mass of the other body ?

• A. 0.6 kg
• B. 0.4 kg
• C. 0.3 kg
• D. 0.2 kg

Answer 1

The correct option is A

0.6 kg

mass of first body, m₁ = 1 kg

mass of second body, m₂ = m (let)

initial velocity of m₁, u₁ = u (let)

final velcoty of m₁, v₁ = $\frac{u}{4}$

initial velocity of m₂ = 0

final velocity of m₂ = v (let)

according to law of conservation of momentum for elastic collision

(1 x u) + (m x 0) = (1 x $\frac{u}{4}$) + (m x v)

v = $\frac{3u}{4m}$----------- (1)

according to law of conservation of energy for elastic collision

(1 x u²) + (m x 0) = (1 x ($\frac{u}{4}$)²) + (mv²)

v² = $\frac{15\left(u^2\right)}{16m}$ ------------(2)

from (1) and (2) we will get

m = 0.6 kg