Question

A force of $20\mathrm{N}$ acts on a body and the body moves through $1\mathrm{m}$ at an angle of $45°$ to the direction of the force. The work done by the force is

• A. $10\sqrt{2}\mathrm{J}$
• B. $\frac{10}{\sqrt{2}}\mathrm{J}$
• C. $-10\sqrt{2}\mathrm{J}$
• D. $\frac{-10}{\sqrt{2}}\mathrm{J}$

Answer 1

The correct option is A

$10\sqrt{2}\mathrm{J}$

Step 1: Given data

Force acting on the body, $F=20\mathrm{N}$

Displacement of the body, $S=1\mathrm{m}$

Angle made by the force with the ground, $\theta =45°$

Step 2: Calculating work done

The work done on a body by a force $F$ on displacing it through a distance of $S$

$W=FS\cos \theta$

where $\theta$ is the angle made by the force with the ground.

Substituting the given values, the work done by the force is

$$\begin{gathered} W=\left(20\right)\left(1\right)\cos 45° \\ =20\times \frac{1}{\sqrt{2}}[\cos 45°=\frac{1}{\sqrt{2}}] \\ =\frac{20}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}} \\ =10\sqrt{2} \end{gathered}$$

Thus, the work done by the force is $10\sqrt{2}\mathrm{J}$.

Hence, option (A) is correct.