Question

A A stone is rotated steadily in a horizontal circle with a period T by a string of length l. If the tension in the string is kept constant and l increases by 1%, what is the percentage change in T A stone is rotated steadily in a horizontal circle with a period T by a string of length l. If the tension in the string is kept constant and l increases by 1%, what is the percentage change in T A stone is rotated steadily in a horizontal circle with a period T by a string of length l. If the tension in the string is kept constant and l increases by 1%, what is the percentage change in T

• A. 1%
• B. 0.5%
• C. 2%
• D. 0.25%

Answer 1

Answer: (B)

0.5%

Answer 2

Tension $= \frac{m4\pi^{2}l}{T^{2}}$ ∴ $l \propto T^{2}$ or $T \propto \sqrt{l}$

[Tension and mass are constant]

Percentage change in Time period $= \frac{1}{2}$ (percentage change in length) [If % change is very small]

$= \frac{1}{2}(1\%) = 0.5\%$