The acceleration due to gravity is measured on the surface of ear… - Vidyadip

MCQ

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

✓

Answer

Correct option: D.

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

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

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

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

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

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

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

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