Q186 / 200 · AP EAMCET 2001 · Physics

A body of mass $6 \mathrm{~kg}$ is under a force which causes displacement in it given by $s=\frac{t^2}{4}$ metres where $t$ is time. The work done by the force in 2 seconds is

  • A
    $12 \mathrm{~J}$
  • B
    $9 \mathrm{~J}$
  • C
    $6 \mathrm{~J}$
  • Correct answer
    D
    $3 \mathrm{~J}$

Solution

$m=6 \mathrm{~kg}, s=\frac{t^2}{4}$ Work done $(W)=$ Force $\times$ Displacement $=m a \times s$ Displacement, $s=\frac{t^2}{4}$ $\therefore$ Acceleration, $a=\frac{d v}{d t}=\frac{d}{d t}\left(\frac{d s}{d t}\right)$ $=\frac{d}{d t}\left[\frac{d}{d t}\left(\frac{t^2}{4}\right)\right]=\frac{d}{d t}\left(\frac{2 t}{4}\right)=\frac{1}{2}$ $\begin{aligned} \therefore \quad W & =6 \times \frac{1}{2} \times \frac{t^2}{4}=\frac{3}{4} t^2=\frac{3}{4}(2)^2 \\ & =\frac{3}{4} \times 4=3 \mathrm{~J}\end{aligned}$

Hence, the correct answer is option: 'D'.

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