Question

A body moves from a position $r_{1}=\left(2 \hat{i} - 3 \hat{j} - 4 \hat{k}\right) \, m$ to a position, $r_{2}=\left(\right.3\hat{i}-4\hat{j}+5\hat{k}\left.\right) \, m$ under the influence of a constant force $F=\left(4 \hat{i} + \hat{j} + 6 \hat{k}\right) \, N$ . The work done by the force is

• A. 57 J
• B. 58 J
• C. 59 J
• D. 60 J

Answer 1

Answer: (A)

Given, $r_{1}=2\hat{i}-3\hat{j}-4\hat{k}$
And $ \, \, r_{2}=3\hat{i}-4\hat{j}+5\hat{k}$
Now, $r_{2}-r_{1}=\hat{i}-\hat{j}+9\hat{k}$
And $F=4\hat{i}+\hat{j}+6\hat{k}$
$\therefore \, \, \, $ work done = F.r
$W=\left(4 \hat{i} + \hat{j} + 6 \hat{k}\right).\left(\right.\hat{i}-\hat{j}+9\hat{k}$ )
$ \, \, =4-1+54=57 \, J$