Two constant forces ${\vec{F}}_{1} and {\vec{F}}_{2}$ act on a body of mass 8 kg. These forces displace the body from point P (1, -2, 3) to Q (2, 3, 7) in 2s starting from rest. Force ${\vec{F}}_{1}$ is of magnitude 9 N and is acting along vector $(2 \hat{i} - 2 \hat{j} + \hat{k})$ . Work done by the force ${\vec{F}}_{2}$ is

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180 J

80 J

-180 J

-80 J

answer is D.

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Detailed Solution

$\begin{matrix} \vec{s} = \hat{i} + 5 \hat{j} + 4 \hat{k} = \frac{1}{2} (\frac{{\vec{F}}_{1} + {\vec{F}}_{2}}{m}) (2)^{2} . . . . . . . . . . . (i) \\ {\vec{F}}_{1} = \frac{9 (2 \hat{i} - 2 \hat{j} + \hat{k})}{\sqrt{2^{2} + 2^{2} + 1}} = 6 \hat{i} - 6 \hat{j} + 3 \hat{k} . . . . . . . . . . . (ii) \end{matrix}$
From Eqs.(i) and (ii), $\vec{F_{2}} = - 2 \hat{i} + 26 \hat{j} + 13 \hat{k})$
Work done by ${\vec{F}}_{2} : W = {\vec{F}}_{2} \cdot \vec{s} \cdot = 180 J$