The acceleration due to gravity is found upto an accuracy of 4% on a… | JEE Main 2021 (26 Aug, Shift 2)

Q89JEE Main 2021 · 26 AUG · SHIFT 2Difficult

Errors in Measurement

The acceleration due to gravity is found upto 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 is ..............%

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Answer: 14

Pendulum energy $E = \tfrac{1}{2}m\omega^2A^2 = \tfrac{1}{2}m\dfrac{g}{L}(L\theta)^2 = \tfrac{1}{2}mgL\theta^2$ .
From $T = 2\pi\sqrt{L/g}$ : $L = \dfrac{gT^2}{4\pi^2}$ , so $E \propto g^2T^2$ (for fixed $m$ , $\theta$ ).
$\dfrac{\Delta E}{E} = 2\dfrac{\Delta g}{g} + 2\dfrac{\Delta T}{T} = 2(4) + 2(3)$
$= 14\%$

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Errors in Measurement question from JEE Main 2021 (26 Aug, Shift 2)

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