Question

In one of the exercises to strengthen the wrist and fingers, a person squeezes and releases a soft rubber ball. Is the work done on the ball positive, negative or zero (i) during compression (ii) During expansion?

• A. While compressing; W_F = positive; while expanding, W_F = positive
• B. While compressing; W_F = Negative; while expanding, W_F = Negative
• C. While compressing; W_F = positive; while expanding, W_F = Negative
• D. While compressing; W_F = Negative; while expanding, W_F = positive

Answer 1

The correct option is C

While compressing; W_F = positive; while expanding, W_F = Negative

While compressing the ball, the force is applied towards the centre of the ball by the human.

The outer surface on which force was being applied is pushed towards the centre of the ball because of this force so work done by this force has to be positive as the object is displaced in the same direction in which the force is applied.

Angle between Force and displacement = $0^{\circ }$

$\Rightarrow cos{0}^{\circ }=1$

$W=F.s.cos\theta$

= $F.s(\because cos{0}^{\circ }=1)$

∵ F and s are just magnitudes of force and displacement so they will be positive. $\Rightarrow w=+ve$ Now during expansion This is the tricky part. Remember the ball is squeezed. You are slowly letting it expand on its own. Your hands are preventing it from expanding suddenly, so still you are applying force inwards towards the centre but this time the boundaries of the ball on which force is being applied is moving outward, away from the centre.

As $\theta ={180}^{\circ }$

$cos{180}^{\circ }=-1$

$W=F.s(-1)=negative$