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Standard VIII

Mathematics

Dimensional Analysis

In a simple p...

Question

In a simple pendulum experiment for the determination of acceleration due to gravity, time period is measured with an accuracy of $0.2$ % while length was measured with an accuracy of $0.5$ %. The percentage accuracy in the value of $g$ so obtained is

0.25

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0.7

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0.9

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1.0

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Solution

The correct option is C $0.9$ %
$T = 2 π \sqrt{\frac{l}{g}}, g \propto \frac{l}{T^{2}}$
$∴ \frac{Δ g}{g} \times 100 = 0.5$ % $+ 2 \times 0.2$ % $= 0.9$ %

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In a simple pendulum experiment for the determination of acceleration due to gravity, time period is measured with an accuracy of 0.2% while length was measured with an accuracy of 0.5%. The percentage accuracy in the value of g so obtained is

The correct option is C 0.9%T=2π√lg, g∝lT2∴Δgg×100=0.5% +2×0.2% =0.9%

In a simple pendulum experiment for the determination of acceleration due to gravity, time period is measured with an accuracy of $0.2$ % while length was measured with an accuracy of $0.5$ %. The percentage accuracy in the value of $g$ so obtained is

The correct option is C $0.9$ %
$T = 2 π \sqrt{\frac{l}{g}}, g \propto \frac{l}{T^{2}}$
$∴ \frac{Δ g}{g} \times 100 = 0.5$ % $+ 2 \times 0.2$ % $= 0.9$ %