Two blocks A and B have masses `m` and `4m`, respectively. Each one is acted upon by a force `F`. If they acquire the same kinetic energy in time `t_A` and `t_B`, then `(t_A)//(t_B)` is

Options

A. 2
B. `(1)/(2)`
C. `3`
D. `(1)/(3)`

Answer

B

Explanation

`A:``a_A=(F)/(m)`,`B:``a_B=(F)/(4m)`
`s_A=(1)/(2)a+_At_A^2`,`s_B=(1)/(2)a_Bt_B^2`
`W_A=W_B=K-0`
`Fs_A=Fs_Bimplies(1)/(2)a_At_A^2=(1)/(2)a_Bt_B^2`
`(t_A)/(t_B)=sqrt((a_B)/(a_A))=(1)/(2)`