MHT CET · Physics · Motion In Two Dimensions
A body performing uniform circular motion of radius ' \(R\) ' has frequency ' \(n\) '. Its centripetal acceleration per unit radius is proportional to \((n)^x\). The value of \(x\) is
- A 1
- B 2
- C -1
- D -2
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Centripetal acceleration is given by,
\(\begin{aligned}
& \mathrm{a}_{\mathrm{c}}=\omega^2 \mathrm{R} \\
& \frac{\mathrm{a}_{\mathrm{c}}}{\mathrm{R}}=(2 \pi \mathrm{n})^2 \\
& \frac{\mathrm{a}_{\mathrm{c}}}{\mathrm{R}}=4 \pi^2 \mathrm{n}^2
\end{aligned}\)
Comparing the above result with \((\mathrm{n})^{\mathrm{x}}\)
\(x=2\)
\(\begin{aligned}
& \mathrm{a}_{\mathrm{c}}=\omega^2 \mathrm{R} \\
& \frac{\mathrm{a}_{\mathrm{c}}}{\mathrm{R}}=(2 \pi \mathrm{n})^2 \\
& \frac{\mathrm{a}_{\mathrm{c}}}{\mathrm{R}}=4 \pi^2 \mathrm{n}^2
\end{aligned}\)
Comparing the above result with \((\mathrm{n})^{\mathrm{x}}\)
\(x=2\)
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