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

Answer: (D)

$F \propto s^{-1 / 3}$
i.e., acceleration $a \propto s^{- 1 / 3}$
or $v\frac{\text{d} \textit{v}}{\text{d} \textit{s}}=\text{K}\textit{s}^{- 1 / 3}\text{ or}$ $\text{v}^{2} \propto \text{s}^{2 / 3}$
or $\textit{v} \propto \textit{s}^{1 / 3}$
Now $\textit{P}=\textit{F.v}$
or $\textit{P} \propto s^{- 1 / 3}\text{. }\textit{s}^{1 / 3}\text{ or }\textit{P} \propto s^{0}$
i.e., power is independent of s.