Question

A body performing uniform circular motion of radius $R$ has frequency $n$. Its centripetal acceleration is

• A. $8\pi^2 nR^2$
• B. $4\pi^2 n^2 R$
• C. $4\pi^2 n^2 R^2$
• D. $8\pi^2 n^2 R$

Hint:

You can use standard dimensional analysis to double-check your answer quickly! Acceleration must have dimensions of $\text{LT}^{-2}$. Frequency $n$ has units of $\text{s}^{-1}$ ($\text{T}^{-1}$) and radius $R$ has units of $\text{m}$ ($\text{L}$). Checking option (B): $n^2 R \rightarrow (\text{s}^{-2})(\text{m}) = \text{m/s}^2$. This matches the dimensions of acceleration perfectly!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Verify which expression for centripetal acceleration is dimensionally consistent using standard dimensional analysis.

Step 2: Key Formula or Approach:
Acceleration has dimensions of LT⁻². Frequency n has dimensions T⁻¹, and radius R has dimensions L. Combine these to test each candidate expression.

Step 3: Detailed Explanation:
Testing option (B): n²R yields (T⁻¹)² × L = T⁻²L = LT⁻², which perfectly matches the dimensions of acceleration. Other options produce mismatched dimensions like LT⁻¹ or L²T⁻². Dimensional analysis provides a rapid independent verification without recalling the exact formula, serving as an excellent exam double-check.

Step 4: Final Answer:
The expression n²R is dimensionally correct for acceleration.