Question

The angle between force and displacement is $\theta$. For what value of $\theta$ is work done zero

• A. $30°$
• B. $45°$
• C. $180°$
• D. $90°$

Answer 1

The correct option is D

$90°$

Step 1: Formula of work done

$W=force\left(f\right)\times displacement\left(s\right)\times \cos \theta$

Step 2: Explanation for the correct option

Option D:

$$\begin{gathered} \theta =90° \\ \cos 90°=0 \end{gathered}$$

So, the work done is zero.

Step 3: Explanation for the incorrect options

Option A:

$$\begin{gathered} \theta =30° \\ \cos 30°=0.866 \end{gathered}$$

So, the work done is non-zero.

Option B:

$$\begin{gathered} \theta =45° \\ \cos 45°=0.707 \end{gathered}$$

So, the work done is non-zero.

Option C:

$$\begin{gathered} \theta =180° \\ \cos 180°=-1 \end{gathered}$$

So, the work done is non-zero.

Hence, the correct option is D.