Question

Two bodies have masses in the ratio 5 : 1 and their kinetic energies are in the ratio 125 : 9. Calculate the ratio of their velocities.

Two bodies A and B have masses in the ratio 5 : 1 and their kinetic energies are in the ratio 125 : 9. Find the ratio of their velocities.

Answer 1

Given `m_A/m_B = 5/1`

`K_A/K_B = 125/9`

Since `K_A/K_B = (1/2 m_A V_A^2)/(1/2 m_B V_B^2)`

= `(m_A/m_B)· V_A^2/V_B^2`

`125/9 = 5/1 ⋅ V_A^2/V_B^2 or V_A/V_B = sqrt(25/9)`

= `5/3`

The ratio of velocities of A and B is 5 : 3.