Question

Two balls with masses in the ratio of 1:2 moving in opposite direction have a head-on elastic collision. If their velocities before impact were in the ratio of 3:1, then velocities after impact will have the ratio :

A. 5:3
B. 7:5
C. 4:5
D. 2: 3

Answer 1

In an elastic collision between two balls with masses in the ratio of 1:2 and velocities in the ratio of 3:1, the velocities after impact will have a ratio of 3:5, which corresponds to answer choice C.

Step-by-step explanation:

In an elastic collision, both the momentum and kinetic energy of the system are conserved. Let's denote the velocities of the two balls before collision as v1 and v2, and their masses as m1 and m2 respectively. We are given that m1/m2 = 1/2 and v1/v2 = 3/1.

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision:

m1*v1 + m2*(-v2) = m1*(-v1) + m2*v2

Simplifying this equation, we get:

(m1+m2)*v1 + (m2-m1)*v2 = 0

Substituting the given ratios, we have:

(3/2 + 2)*(3/1) + (2 - 3/2)*v2 = 0

Solving for v2, we find:

v2 = -3/5 m/s

Therefore, the velocities after impact will have the ratio of 3:5, which gives us the answer choice C. 4:5.