Question

Work done when a force of (7\[\hat i\] - 4\[\hat j\] - 4\[\hat k\]) N moves a body through a distance of 10 metre in its own direction is ______.

Options

• 160 J

• 120 J

• 90 J

• 10 J

Answer 1

Work done when a force of (7\[\hat i\] - 4\[\hat j\] - 4\[\hat k\]) N moves a body through a distance of 10 metre in its own direction is 90 J.

Explanation:

W = \[\vec F\] . \[\vec s\] = Fs cos θ

For force causing displacement in its own direction θ = 0°

\[\therefore\] W = Fs = \[\left(\sqrt{\left(7\right)^{2}+\left(-4\right)^{2}+\left(-4\right)^{2}}\right)\times10\]

= \[\left(\sqrt{49+16+16}\right)\times10=9\times10=90\mathrm{J}\]