Question

A stone is rotated steadily in a horizontal circle with a time period $T$ by means of a string of length $\ell$. If the tension in the string is kept constant and length $\ell$ increase by $1\%$ then percentage change in time period $T$ is

• A. $1\%$
• B. $0.5\%$
• C. $2\%$
• D. $0.25\%$

Answer 1

Answer: (B)

$0.5\%$

Tension in the string $F=m{a}_r=ml{w}^2$ where $w=\frac{2\pi }{T}$

$\therefore$ $F=ml\times \frac{4{\pi }^2}{T^2}$

$⟹$ $T=2\pi \sqrt{\frac{ml}{F}}$

$⟹$ Percentage change in time period $\frac{\Delta T}{T}\times 100=\frac{1}{2}\frac{\Delta l}{l}\times 100$

$\therefore$ $\frac{\Delta T}{T}\times 100=\frac{1}{2}\times 1$ % $=0.5$ %