Two bodies A and B have masses 20 kg and 5 kg respectively. Each one is acted upon by a force of 4 kg wt. If they acquire the same kinetic energy in times `t_A and t_B` then the ratio `(t_A)/(t_B)` is   

Options

A. `1/2`
B. `2`
C. `2/5`
D. `5/6`

Answer

B

Explanation

Here, `m_A = 20 kg, m_B = 5 kg`
As force = 40 N
`:. a_A = 2 ms^(-2) and a_B = 8 ms^(-2)`
Also `K_A = K_B` (given)
`:. 1/2 m_A (a_A t_A)^2 = 1/2 m_B (a_B t_B)^2`
or `1/2 xx 20 xx 4t_A^2 = 1/2 xx 5 xx 64 t_B^2`
or `(t_A^2)/(t_B^2) = (1/2 xx 5 xx 64)/(1/2 xx 20 xx 4) = 4/1 " or " (t_A)/(t_B) = 2`.