Question

A particle moves from position $r_{1}=\left(3 \hat{i} + 2 \hat{j} - 6 \hat{k}\right) \, m$ to position $r_{2}=\left(14 \hat{i} + 13 \hat{j} + 9 \hat{k}\right) \, m$ under the action of a force $\left(4 \hat{i} + \hat{j} - 3 \hat{k}\right) \, N,$ then the work done is

• A. $46 \, J$
• B. $56 \, J$
• C. $86 \, J$
• D. $10 \, J$

Answer 1

Answer: (D)

Given, $r_{1}=\left(3 \hat{i} + 2 \hat{j} - 6 \hat{k}\right) \, m$
$r_{2}=\left(14 \hat{i} + 13 \hat{j} + 9 \hat{k}\right) \, m$
$F=\left(4 \hat{i} + \hat{j} - 3 \hat{k}\right) \, N$
Displacement, $s=r_{2}-r_{1}$
$=\left(14 \hat{i} + 13 \hat{j} + 9 \hat{k}\right)-\left(3 \hat{i} + 2 \hat{j} - 6 \hat{k}\right)$
or, $s=11\hat{i}+11\hat{j}+15\hat{k}$
$\therefore $ Work done, $W=F.s$
$=\left(4 \hat{i} + \hat{j} - 3 \hat{k}\right)\cdot \left(11 \hat{i} + 11 \hat{j} + 15 \hat{k}\right)$
$=44+11-45$
or $W=10 \, J$