A pendulum is suspended in a lift and its period of oscillation when lift is stationary is&nbsp

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13.Oscillations

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A pendulum is suspended in a lift and its period of oscillation when the lift is stationary is $T_0$. What must be the acceleration of the lift for the period of oscillation of the pendulum to be $T_0/2$ ?

A

$2g$ downward

B

$2g$ upward

C

$3g$ downward

D

$3g$ upward

Solution

$\mathrm{T}_{0}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}$

$\frac{\mathrm{T}_{0}}{2}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}+\mathrm{a}}}$

$\frac{2 \pi \sqrt{\frac{\ell}{\mathrm{g}}}}{2}=2 \pi \sqrt{\frac{\ell}{\mathrm{g}+\mathrm{a}}}$

$\frac{1}{4 g}=\frac{1}{g+a}$

$g+a=4 g$

$a=3 g$ upward

Standard 11

Physics

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