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A body is thrown vertically upwards. If ...

A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is.

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

Text Solution

Verified by Experts

The correct Answer is:
B
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) ` .
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