If the length of the pendulum in a pendulum clock increases by $0.1\, \%$,then the error in time per day is: (in $s$)

The time period of a simple pendulum of length $L$ is $T_1$. The time period of a uniform rod of the same length $L$ suspended from one end and oscillating in a vertical plane is $T_2$. The amplitude of oscillation is small in both cases. Then the ratio $\frac{T_1}{T_2}$ is:

In a simple pendulum,the breaking strength of the string is double the weight of the bob. The bob is released from rest when the string is horizontal. The string breaks when it makes an angle $\theta$ with the vertical.

$A$ simple pendulum is hanging from a peg inserted in a vertical wall. Its bob is stretched in a horizontal position from the wall and is left free to move. The bob hits the wall,and the coefficient of restitution is $\frac{2}{\sqrt{5}}$. After how many collisions will the amplitude of vibration become less than $60^\circ$?

$A$ 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?

The time period of oscillation of a simple pendulum of length $L$ suspended from the roof of a vehicle,which moves without friction down an inclined plane of inclination $\alpha$,is given by: