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JEE Main 2015 · Simple Pendulum

Simple Pendulum question from JEE Main 2015

Q77JEE Main 2015Medium

Simple Pendulum

The period of oscillation of a simple pendulum is $T = 2\pi\sqrt{\frac{L}{g}}$ . Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is:

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Answer: (d)

$\frac{\Delta g}{g} = \frac{\Delta L}{L} + 2\frac{\Delta t}{t}$ .
$\frac{\Delta L}{L} = \frac{0.1}{20.0} = 0.5\%$ ; $2\frac{\Delta t}{t} = 2 \times \frac{1}{90} \approx 2.2\%$ .
Total $\approx 2.7\% \approx 3\%$ .
So the answer is (d) $3\%$ .

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