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. \(S^0\)

Hint:

When \(F \propto S^{-1/3}\), \(v \propto S^{1/3}\), so power is constant.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Power = Fv, need v in terms of S.
Step 2: Detailed Explanation:
\(F \propto S^{-1/3} \rightarrow a \propto S^{-1/3}\)
\(v \frac{dv}{dS} \propto S^{-1/3} \rightarrow v\,dv \propto S^{-1/3}\,dS\)
Integrate: \(v^2 \propto S^{2/3} \rightarrow v \propto S^{1/3}\)
\(P = Fv \propto S^{-1/3} \times S^{1/3} \propto S^0\)
Step 3: Final Answer:
Power is independent of displacement.