$A$ 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?

$A$ second's pendulum is placed in a space laboratory orbiting around the earth at a height $3R$,where $R$ is the radius of the earth. The time period of the pendulum is

Frequency $f$ of a simple pendulum depends on its length $\ell$ and acceleration $g$ due to gravity according to the following equation $f = \frac{1}{2 \pi} \sqrt{\frac{g}{\ell}}$. $A$ graph between which of the following quantities is a straight line?

$A$ simple pendulum of length $2 \ m$ is given a horizontal push through an angular displacement of $60^{\circ}$. If the mass of the bob is $200 \ g$,the angular velocity of the bob will be (Take acceleration due to gravity $g = 10 \ m/s^2$).

$A$ simple pendulum of length $1 \ m$ and having a bob of mass $100 \ g$ is suspended in a car, moving on a circular track of radius $100 \ m$ with uniform speed $10 \ m/s$. If the pendulum makes small oscillations in a radial direction about its equilibrium position, then its time period is given by $T = 2\pi / \alpha^{1/4}$. The value of $\alpha$ is (Take $g = 10 \ m/s^2$)

$A$ child is sitting on a swing which performs $S.H.M$. It has minimum and maximum heights from the ground of $0.75 \,m$ and $2 \,m$ respectively. Its maximum speed will be $\left[g=10 \,m/s^2\right]$