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Home  >>  JEEMAIN and AIPMT  >>  Physics  >>  Class11  >>  Work, Power and Energy
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A body of mass 3 kg under constant force which causes a displacement $s$ in meters in it given by $s=\large\frac{1}{3}$$t^2$ work done by the force in $2$ seconds is

\[(a)\;\frac{8}{3}\;J\quad (b)\;\frac{19}{5}\;J \quad (c)\; \frac{5}{19}\;J \quad (d)\;\frac{3}{8}\;J\]

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1 Answer

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$s=\large\frac{1}{3}$$t^2=>\large\frac{ds}{dt}=\frac{2}{3}$$t$
acceleration $=a=\large\frac{d^2s}{dt^2}$
$\qquad=\large\frac{2}{3}$$m/s^2$
Force $=m \times a$
$ \qquad=3 \times \large\frac{2}{3}$$=2N$
$ds=\large\frac{2}{3}$$tdt$
Work done $= \int F ds$
$W=F \int \limits_0^t \large\frac{2}{3} $$t dt$
$\quad=2 \times \large\frac{2}{3} $$ \times \large \frac{t^2}{2} \bigg|_0^2$
$\quad=\large\frac{4}{3} \times \frac{4}{2}$
$\quad=\large\frac{8}{3}$$\;J$
Hence a is the correct answer. 

 

answered Aug 8, 2013 by meena.p
edited Feb 17, 2014 by meena.p
 

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