Two simple pendulums of lengths $L_1$ and $L_2$ have time periods $T_1$ and $T_2$ respectively, where $T_1 > T_2$. What is the time period of a simple pendulum of length $(L_1 - L_2)$?

$A$ pendulum clock keeps correct time at $0^{\circ}C$. If its mean coefficient of linear expansion is $\alpha /^{\circ}C$,what is the loss in seconds per day by the clock if the temperature rises by $t^{\circ}C$?

$A$ simple pendulum keeps correct time at $0^{\circ}C$. At $25^{\circ}C$,it loses $12.5 \, s$ in a day. What is the coefficient of linear expansion of the metal of the pendulum?

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$ from their mean positions,respectively. If the angular accelerations of both pendulums are same,then which expression is correct?

The time period of a simple pendulum inside a stationary lift is $T$. When the lift starts accelerating upwards with an acceleration of $\frac{g}{3}$,the time period of the pendulum will be

Two masses,both equal to $100\, g$,are suspended at the ends of identical light strings of length $\ell = 1.0\, m$,attached to the same point on the ceiling (see figure). At time $t = 0$,they are simultaneously released from rest,one at angle $\theta_1 = 1^o$,the other at angle $\theta_2 = 2^o$ from the vertical. The masses will collide