Question

A force F acting on a body depends on its displacement $S$ as $F\propto S^{1/3}$. The power delivered by $F$ will depend on displacement as:

• A. $S^{2/3}$
• B. $S^{-5/3}$
• C. $S^{1/2}$
• D. $S^0$

Answer 1

The correct option is A $S^{2/3}$

We know Power=$\frac{workdone}{time}$

Also work done = Force $\times$displacement

As given $F\alpha S^{1/3}$

$F=K{S}^{1/3}$------(1) (where $K$= constant of proportionality)

Now Power= $\frac{F\times S}{time}$----(2)

Putting value of 1 in 2 we get

$P=\frac{K{S}^{\frac{2}{3}}}{t}$