1. Tardigrade
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  4. The time period of a simple pendulum is given by T =2 π √(ℓ/ g ) The measured value of the length of pendulum is 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1 s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is:-

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Q. The time period of a simple pendulum is given by $T =2 \pi \sqrt{\frac{\ell}{ g }} $ The measured value of the length of pendulum is $10\,cm$ known to a $1\,mm$ accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1 s resolution. The percentage accuracy in the determination of 'g' using this pendulum is 'x'. The value of 'x' to the nearest integer is:-

JEE MainJEE Main 2021Physical World, Units and Measurements

Solution:

$g=\frac{4 \pi^{2} \ell}{T^{2}}$
$\frac{\Delta g}{g}=\frac{\Delta \ell}{\ell}+2 \frac{\Delta T}{T}=\frac{0.1}{10}+2\left(\frac{\frac{1}{200}}{0.5}\right)$
$\frac{\Delta g}{g}=\frac{1}{100}+\frac{1}{50}$
$\frac{\Delta g}{g} \times 100=3 \%$