Q127 / 160 · AP EAMCET 2023 (15 May Shift 2) · Physics

A body of mass $2 \mathrm{~kg}$ is moving with a constant acceleration of $(2 \hat{i}+3 \hat{j}-\hat{k}) \mathrm{ms}^{-2}$. If the displacement made by the body is $(3 \hat{i}-\hat{j}+2 \hat{k}) \mathrm{m}$ then the work done is

  • A
    $22 \mathrm{~J}$
  • Correct answer
    B
    $2 \mathrm{~J}$
  • C
    $12 \mathrm{~J}$
  • D
    $10 \mathrm{~J}$

Solution

$\begin{aligned} & \text { Mass of body, } m=2 \mathrm{~kg} \\ & \text { acceleration, } a=2 \hat{i}+3 \hat{j}-\hat{k} \\ & \text { displacement, } \vec{s}=3 \hat{i}-\hat{j}+2 \hat{k} \\ & \text { work done, } W=F \cdot S \\ & =m \vec{a} \cdot \vec{s} \\ & =2(2 \hat{i}+3 \hat{j}-\hat{k})(3 \hat{i}-\hat{j}+2 \hat{k}) \\ & =2[6-3-2]=2 J\end{aligned}$

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

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