Time period of a simple pendulum is $$T$$ inside a lift when the lift is stationary. If the lift moves upwards with an acceleration $$\frac{g}{2}$$, the time period of pendulum will be:

When the lift is stationary, the time period of a simple pendulum is $$T = 2\pi\sqrt{\frac{l}{g}}$$.

When the lift accelerates upward with acceleration $$\frac{g}{2}$$, the effective gravitational acceleration inside the lift increases to $$g_{\text{eff}} = g + \frac{g}{2} = \frac{3g}{2}$$. This is because the pseudo force in the non-inertial frame of the lift acts downward, adding to gravity.

The new time period becomes $$T' = 2\pi\sqrt{\frac{l}{g_{\text{eff}}}} = 2\pi\sqrt{\frac{l}{\frac{3g}{2}}} = 2\pi\sqrt{\frac{2l}{3g}}$$.

We can write this as $$T' = 2\pi\sqrt{\frac{l}{g}} \times \sqrt{\frac{2}{3}} = T\sqrt{\frac{2}{3}}$$.