Question

Work done is zero when :

• A. force causes displacement in its own direction.
• B. force causes displacement in opposite direction.
• C. force causes displacement in a perpendicular direction.
• D. force causes displacement at an acute angle.

Answer 1

The correct option is C

force causes displacement in a perpendicular direction.

1. When force is at an angle to the displacement, work done is given as,

$$\begin{gathered} W=F\times s\times \cos \theta \\ where, \\ W\to Workdone \\ F\to Force \\ s\to Displacementofthepointofapplicationinthedirectionofforce \\ \theta \to Anglebetweenforceanddisplacement \end{gathered}$$

2. Based on the value of the angle between force and displacement work done can be positive, negative, or zero.

Value of $\theta$	Value of $\cos \theta$	Nature of work done	Example
$0\le \theta <90°$	$0<\cos \theta \le 1$	Positive	Work done by a man pushing a car when its engine stops working.
$\theta =90°$	$\cos \theta =0$	Zero	Work done by a porter (coolie) carrying a load on his head and walking, work done by planets revolving around the Sun.
$90°<\theta \le 180°$	$-1\le \cos \theta <0$	Negative	Work done by friction.

3. Hence, work done is zero when a force causes displacement in a perpendicular direction.

Hence, option C is correct.