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(D) Given: Length of simple pendulum $L = 1 \,m$,acceleration of elevator $a = 2 \,m/s^2$,and acceleration due to gravity $g = 10 \,m/s^2$.When an ele

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$\frac{\pi}{\sqrt{3}} \,s$

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(D) Given: Length of simple pendulum $L = 1 \,m$,acceleration of elevator $a = 2 \,m/s^2$,and acceleration due to gravity $g = 10 \,m/s^2$.When an elevator moves upward with an acceleration $a$,the effective acceleration due to gravity $g_{eff}$ is given by $g_{eff} = g + a$.Substituting the values,$g_{eff} = 10 + 2 = 12 \,m/s^2$.The time period $T$ of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L}{g_{eff}}}$.Substituting the values,$T = 2\pi \sqrt{\frac{1}{12}} = 2\pi \frac{1}{\sqrt{4 	imes 3}} = 2\pi \frac{1}{2\sqrt{3}} = \frac{\pi}{\sqrt{3}} \,s$.

$A$ simple pendulum of length $1 \,m$ is freely suspended from the ceiling of an elevator. The time period of small oscillations as the elevator moves up with an acceleration of $2 \,m/s^2$ is (use $g=10 \,m/s^2$).

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