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A body of mass 6kg is under a force whic...

A body of mass `6kg` is under a force which causes displacement in it given by `S= (t^(2))/(4)` maters where `t` is time . The work done by the force in `2` sec is

A

`12 J`

B

`9J`

C

`6J`

D

`3J`.

Text Solution

Verified by Experts

The correct Answer is:
D
Here, `m=6 kg`
Given : `x=(t^2)/(4)`
Velocity, `v=(dx)/(dt) = (2)/(4) t= (t)/(2)`
Acceleration, `a=(dv)/(dt)=(1)/(2)`
`therefore` Force, `F= ma = 6 xx (1)/(2) = 3 N`
`therefore` Work done, `W= int F dx = int_(0)^(2) (3) ((t)/(2)) dt= (3)/(2) [(t^(2) )/(2)]_(0)^(2) = 3` J .
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