A ball is thrown vertically upwards from the ground. If `T_1` and `T_2` are the respective time taken in going up and coming down, and the air resistance is not ignored, then

Options

A. ` t_1 =t_2`
B. ` t_1lt ty_2`
C. `t_1 gtt_2`
D. `t_2-ltt_1`

Answer

B

Explanation

Let (a) be the retarding acceleration acting on body due to air friction. Therefore, effective value of (g) for upward motion, ` g_1 = g+a` and for downward motion, ` g-2 = (g-a) `. We know that,
` t= sqrt ( 2h)/(g_(effective)` or ` t prop 1/(sqrt (g_(effective )1
:. ` t_1 /t_2 = sqrt g_2/g_1` = sqrt ((g-1)/(g+a))) lt 1 ` or ` t_1 lt t_2`.