A force $(5 \hat{\imath}-2 \hat{\jmath}+3 \hat{k}) \mathrm{N}$ acts on a body of mass $2 \mathrm{~kg}$ and…

A force $(5 \hat{\imath}-2 \hat{\jmath}+3 \hat{k}) \mathrm{N}$ acts on a body of mass $2 \mathrm{~kg}$ and displaces it from $(3 \hat{\imath}+2 \hat{\jmath}-\hat{k}) \mathrm{m}$ to $(6 \hat{\imath}-\hat{\jmath}+4 \hat{k}) \mathrm{m} .$ The work done is
  1. 27 J
  2. 18 J
  3. $36 \mathrm{~J}$
  4. $9 \mathrm{~J}$

Solution

$\begin{aligned} & \begin{aligned} \overline{\mathrm{r}}=3 \mathrm{i}-3 \mathrm{j}+5 \mathrm{k}\end{aligned} \\ & \begin{aligned} \text { Work done } & =\overline{\mathrm{F}} . \overrightarrow{\mathrm{r}}\end{aligned} \\ &=(5 \mathrm{i}-2 \mathrm{j}+3 \mathrm{k}) \cdot(3 \mathrm{i}-3 \mathrm{j}+5 \mathrm{k}) \\ &=15+6+15 \\ &=36 \mathrm{~J}\end{aligned}$

Asked in: MHT CET 2020 (15 Oct Shift 2)

Practice more Work Power Energy questions on Aicharya