For a body thrown vertically upwards, if the air resistance is taken into consideration, then the time of rise is

Options

A. Equal to the time of fall
B. Less than the time of fall
C. Greater than the time of fall
D. Twice the time of fall

Answer

B

Explanation

For the sake of qualitative discussion, we will assume that the force of air resistance has a constant value and provides a constant acceleration a opposite to the direction of velocity.Let the initial velocity of ball be u
Time of rise `t_1 =(u)/(g+a) and ` height reached ` =(u^(2))/(2(g+a))`
Time of fall ` t_2` is given by
` (1)/(2) (g-a) t_2^(2) =(u^(2))/(2(g+a)) rArr t_2 =(u)/( sqrt ( g+a) (g-a)) sqrt (( g+a)/(g-a) ) therefore t_2gt t_1 ` because ` (g+a)gt (g-a) ` .