Question:
If force, $F=kv^{n}$ (k is constant) and power delivered is independent of velocity 'v', then n equals to:
If force, $F=kv^{n}$ (k is constant) and power delivered is independent of velocity 'v', then n equals to:
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Power is independent of velocity when the force varies inversely with velocity.
Updated On: Jun 10, 2026
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The Correct Option is C
Solution and Explanation
Step 1: Concept
Power ($P$) is defined as the product of force ($F$) and velocity ($v$), i.e., $P = F \cdot v$.
Step 2: Analysis
Given $F = kv^n$, substitute this into the power formula: $P = (kv^n) \cdot v = kv^{n+1}$.
Step 3: Conclusion
If power is independent of velocity, the exponent of $v$ must be zero: $n+1 = 0$, which means $n = -1$.
Final Answer: (C)
Power ($P$) is defined as the product of force ($F$) and velocity ($v$), i.e., $P = F \cdot v$.
Step 2: Analysis
Given $F = kv^n$, substitute this into the power formula: $P = (kv^n) \cdot v = kv^{n+1}$.
Step 3: Conclusion
If power is independent of velocity, the exponent of $v$ must be zero: $n+1 = 0$, which means $n = -1$.
Final Answer: (C)
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