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n' = 1/(2π)√(k/m). If k is constant and length varies by n%, the change in time period ΔT/T × 100 = ?

1. n/2%
2. n%
3. 2n%
4. n^2%

Correct answer: n/2%

Solution

The time period T is proportional to the square root of the length (T ∝ √L). If the length changes by n%, the fractional change in T is (1/2) × (n/100), which corresponds to n/2% change in T.

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