Question:
A body, performing uniform circular motion of radius 'r', has frequency 'n'. Its centripetal acceleration per unit radius is related as \((\text{n})^{x}\). The value of \(x\) is
A body, performing uniform circular motion of radius 'r', has frequency 'n'. Its centripetal acceleration per unit radius is related as \((\text{n})^{x}\). The value of \(x\) is
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Write the centripetal acceleration using angular velocity and then use omega equal to 2 pi n.
Updated On: Nov 12, 2026
- \(-2\)
- \(-1\)
- \(1\)
- \(2\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
Centripetal acceleration is \(a=\omega^2 r\) and the angular velocity is related to frequency by \(\omega=2\pi n\).
Step 2: Substitute
\(a=(2\pi n)^2 r=4\pi^2 n^2 r\)
Step 3: Per unit radius
\(\dfrac{a}{r}=4\pi^2 n^2\), which is proportional to \(n^2\).
Step 4: Read the power
Comparing with \(n^x\) gives \(x=2\).
Final Answer:
The power of frequency is \(x=2\). \[ \boxed{\text{(D) }2} \]
Centripetal acceleration is \(a=\omega^2 r\) and the angular velocity is related to frequency by \(\omega=2\pi n\).
Step 2: Substitute
\(a=(2\pi n)^2 r=4\pi^2 n^2 r\)
Step 3: Per unit radius
\(\dfrac{a}{r}=4\pi^2 n^2\), which is proportional to \(n^2\).
Step 4: Read the power
Comparing with \(n^x\) gives \(x=2\).
Final Answer:
The power of frequency is \(x=2\). \[ \boxed{\text{(D) }2} \]
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