InterviewSolution
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InterviewSolution
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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-mB. 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 forceD. The particle is not acted upon by a constant force |
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Answer» Correct Answer - 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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