Q155 / 170 · Manipal (MET) 2019 · Physics
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$S^{1 / 2}$
- Correct answerD$S^0$
Solution
$\because F \propto S^{-1 / 3}$ or $a \propto S^{-1 / 3}$
or $V d \nu \propto S^{-1 / 3} d s\left(a=V \cdot \frac{d V}{d s}\right)$
Integrating we have, $V^2 \propto S^{2 / 3}$
or
$V \propto S^{1 / 3}$
Now, power $P \propto F \cdot V \propto S^{-1 / 3} \cdot S^{1 / 3}$ or
$P \propto S^0$
Hence, the correct answer is option: 'D'.