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Standard VIII

Mathematics

Dimensional Analysis

In an experim...

Question

In an experiment, on the measurement of $g$ , using a simple pendulum, the time period was measured with an accuracy of $0.2$ % while the length was measured with an accuracy of $0.5$ %. The percentage accuracy in the value of $g$ thus obtained is

0.7

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0.1

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0.25

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0.9

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Solution

The correct option is B $0.9$ %
Time period of the pendulum is given by $T = 2 π \sqrt{\frac{l}{g}}$
or $g = {(\frac{2 π}{T})}^{2} \cdot l$
$\Rightarrow \frac{△ g}{g} = \frac{△ l}{l} + \frac{2 △ T}{T} = 0.5 + 2 \times 0.2$
Thus percentage error in the value $\frac{△ g}{g} \times 100 = 0.9$ %.

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In an experiment, on the measurement of g, using a simple pendulum, the time period was measured with an accuracy of 0.2% while the length was measured with an accuracy of 0.5%. The percentage accuracy in the value of g thus obtained is

The correct option is B 0.9%Time period of the pendulum is given by T=2π√lg or g=(2πT)2⋅l⇒△gg=△ll+2△TT=0.5+2×0.2 Thus percentage error in the value △gg×100=0.9%.

In an experiment, on the measurement of $g$ , using a simple pendulum, the time period was measured with an accuracy of $0.2$ % while the length was measured with an accuracy of $0.5$ %. The percentage accuracy in the value of $g$ thus obtained is