TS EAMCET · Physics · Rotational Motion
If the length of a thin uniform rod is ' \(L\) ' and the radius of gyration of the rod about an axis perpendicular to its length and passing through one end is \(K\), then \(K: L=\)
- A \(1: \sqrt{3}\)
- B \(1: \sqrt{2}\)
- C \(1: 3\)
- D \(1: 2\)
Answer & Solution
Correct Answer
(A) \(1: \sqrt{3}\)
Step-by-step Solution
Detailed explanation
\(I = \frac{1}{3}ML^2\) \(I = MK^2\) \(MK^2 = \frac{1}{3}ML^2 \implies K^2 = \frac{1}{3}L^2 \implies K = \frac{L}{\sqrt{3}}\) \(K:L = \frac{L}{\sqrt{3}}:L = 1:\sqrt{3}\)
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