1. Tardigrade
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  3. Physics
  4. The period of oscillation of a simple pendulum is given by T=2π√(l/g) where l is about 100 cm and is known to have 1 mm accuracy. The period is about 2 s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is

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Q. The period of oscillation of a simple pendulum is given by $T=2\pi\sqrt{\frac{l}{g}}$ where $l$ is about $100\, cm$ and is known to have $1\, mm$ accuracy. The period is about $2\, s$. The time of $100$ oscillations is measured by a stop watch of least count $0.1\, s.$ The percentage error in g is

Physical World, Units and Measurements

Solution:

$T=2\pi\sqrt{l/g}$
$\Rightarrow T^{2}=4\pi^{2}l/g$
$\Rightarrow g=\frac{4\pi^{2}l}{T^{2}}$
Here $\%$error in $l=\frac{1 mm}{100 cm}\times100$
$=\frac{0.1}{100}\times100=0.1\%$
and $\%$ error in $T=\frac{0.1}{2\times100}\times100$
$=0.05\%$
$\therefore \%$ in $g=\%$ error in $l+2(\%$ error in $T)$