Acceleration due to gravity is measured on surface of earth by using a simple pendulum. If α and β

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1.Units, Dimensions and Measurement

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The acceleration due to gravity is measured on the surface of earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively, then percentage error in the measurement of acceleration due to gravity is ................

A

$\left(\alpha+\frac{1}{2} \beta\right) \times 100$

B

$(\alpha-2 \beta)$

C

$(2 \alpha+\beta) \times 100$

D

$(\alpha+2 \beta) \times 100$

Solution

$\frac{\Delta L}{L}=\alpha \quad \frac{\Delta T}{T}=\beta$

$\frac{\Delta g}{g}=?$

$r=2 \pi \sqrt{\frac{L}{g}}$

$\frac{\Delta g}{g}=4 \pi^2 \frac{L}{T^2}$

$\frac{\Delta g}{g}=\left(\frac{\Delta L}{L}+2 \frac{\Delta T}{T}\right)$

$\frac{\Delta g}{g}=(\alpha+2 \beta) \times 100$

Standard 11

Physics

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