The time period of a simple pendulum of length $L$ as measured in an elevator descending with acceleration $\frac{g}{3}$ is
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(c)The effective acceleration in a lift descending with acceleration $\frac{g}{3}$ is ${g_{eff}} = g - \frac{g}{3} = \frac{{2g}}{3}$
$T = 2\pi \sqrt {\left( {\frac{L}{{{g_{eff}}}}} \right)} $$ = 2\pi \sqrt {\left( {\frac{L}{{2g/3}}} \right)} $$ = 2\pi \sqrt {\left( {\frac{{3L}}{{2g}}} \right)} $
$T = 2\pi \sqrt {\left( {\frac{L}{{{g_{eff}}}}} \right)} $$ = 2\pi \sqrt {\left( {\frac{L}{{2g/3}}} \right)} $$ = 2\pi \sqrt {\left( {\frac{{3L}}{{2g}}} \right)} $
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