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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
Let initial velocity = u
time to rise `t_1 = (u)/((g+a))`
maximum height reached
`h = (u^2)/(2(g+a))`
For time to all
`1/2 (g - a)t_2^2 = (u^2)/(2(g + a))`
`rArr t_2^2 = (2u^2)/(2(g^2 - a^2)) rArr t_2 (u)/(sqrt(g^2 - a^2))`
`t_2 = (u)/((g+a)) sqrt((g+a)/(g-a)) rArr t_2 = t_1 sqrt((g+a)/(g-a))`
`therefore t_2 gt t_1`
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