Q 11-01-189JEE MainJEE Main 2021 (26 Aug, Shift 2)Medium
The acceleration due to gravity is found up to an accuracy of $4\%$ on a planet. The energy supplied to a simple pendulum of known mass $m$ to undertake oscillations of time period $T$ is being estimated. If time period is measured to an accuracy of $3\%$, the accuracy to which $E$ is known as ______ $\%$
Numerical value type. Enter your answer.
Answer: 14
For a given angular amplitude $\theta_0$, $E = \frac{1}{2}mgl\theta_0^2$ and $l = \dfrac{gT^2}{4\pi^2}$, so
$$E = \frac{mg^2T^2\theta_0^2}{8\pi^2} \propto g^2T^2$$
$$\frac{\Delta E}{E} = 2\frac{\Delta g}{g} + 2\frac{\Delta T}{T} = 2(4\%) + 2(3\%) = 14\%$$
Solution by Sreeraj P, M.Sc Physics