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The motion of a particle of mass m is gi...

The motion of a particle of mass m is given by x=0 for `t lt 0` s, x (t) = `A sin 4pit for 0 lt t(1//4) s (A gt 0)` and x=0 for `t gt (1//4)` s Which of the following statement(s) is (are) true?

A

The force at `t=(1//8)` s on particle is `-16pi^(2)` A-m

B

The particle is acted upon by an impulse of magnitude `(4pi^(2) A-m)` at t=0 s and `t=(1//4)` s.

C

The particle is not acted upon by any force

D

The particle is not acted upon by a constant force

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
For `0 lt t lt 1/4`
`x=Asin 4pit`
`v=(dx)/(dt)=4piA cos4pit`
`a=(dv)/(dt)=16pi^(2)A sin 4pit`
At `t=1/8 s`
`a=-16pi^(2)A sin4pixx1/8=-16pi^(2)A`
`F=ma=-16pi^(2)A-m`
Impulse = change in linear momentum
`=Fxxt=-16pi^(2)A-mxx1/4=-4pi^(2)A-m`
Impulse or change in linear momentum is the same at t=0 or `1/4` s
Force F depends upon A which is not constant therefore particle is not acted upon by a constant force.
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