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.

Explanation

Given ` (m_A)/(m_B) = 5/1 , (K_A)/(K_B) = (125)/(9 )`
Since ` (K_A)/(K_B) = (1/2 m_A V_(2)^(2))/(1/2 m_B V_(B)^(2)) = ((m_A)/(m_B)) . (V_(2)^(2))/(V_(B)^(2))`
` ( 125)/(9) = 5/1 . (V_(A)^(2))/(V_(B)^(2))`
` or (V_A)/(V_B) = sqrt((25)/(9))= 5/3`
Ratio of velocities of A and B is 5: 3.