QJEEM21Phafd0: JEE Main 2021 Physics - Class 11 JEEM21Phafd0 Solution: A particle of mass M originally at rest is subjected to a force …

Question

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A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

F = {F_0}\left[ {1 - {{\left( {{{t - T} \over T}} \right)}^2}} \right]

Where F₀ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :

Accepted Answer

At t = 0, u = 0

a = {{{F_0}} \over M} - {{{F_0}} \over {M{T^2}}}{(t - T)^2} = {{dv} \over {dt}}

\int\limits_0^v {dv = \int\limits_{t = 0}^{2T} {\left( {{{{F_0}} \over M} - {{{F_0}} \over {M{T^2}}}{{(t - T)}^2}} \right)dt} }

V = \left[ {{{{F_0}} \over M}t} \right]_0^{2T} - {{{F_0}} \over {M{T^2}}}\left[ {{{{t^3}} \over 3} - {t^2}T + {T^2}t} \right]_0^{2T}

\Rightarrow

V = {{4{F_0}T} \over {3M}}

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