PYQ NEET- Units Of Measurement L-5

Question: The percentage error in the measurement of $\mathrm{g}$ is : (Given that $\left.g=\frac{4 \pi^2 L}{T^2}, L=(10 \pm 0.1) \mathrm{cm}, T=(100 \pm 1) \mathrm{s}\right)$#

A) $7 %$

B) $2 %$

C) $5 %$

D) $3 %$

Answer: $3 %$#

Solution:#

Given $g=\frac{4 p^2 L}{T^2}$ Fractional error in value of $\mathrm{g}$ $$ \begin{aligned} & \frac{\Delta g}{g}=\frac{\Delta L}{L}+2 \frac{\Delta T}{T} \ & \Rightarrow \frac{\Delta g}{g} \times 100=\frac{\Delta L}{L} \times 100+2 \frac{\Delta T}{T} \times 100 \ & \Rightarrow \frac{\Delta g}{g} \times 100=\frac{0.1}{10} \times 100+2 \times \frac{1}{100} \times 100=3 % \end{aligned} $$

Hence, percentage error in measurement of $\mathrm{g}$ is $3 %$