$A$ pendulum has a length of $0.4 \ m$ and a maximum speed of $4 \ m/s$. When the string makes an angle of $30^{\circ}$ with the horizontal,its speed will be: $\left[\sin \frac{\pi}{6} = \cos \frac{\pi}{3} = 0.5 \text{ and } g = 10 \ m/s^{2}\right]$

The bob of a simple pendulum performs $SHM$ with period $T$ in air and with period $T_1$ in water. The relation between $T$ and $T_1$ is (neglect friction due to water,density of the material of the bob is $\frac{9}{8} \times 10^3 \ kg/m^3$,density of water is $1 \ g/cc$):

$A$ small sphere of radius $r$ is placed on a concave surface of radius of curvature $R$ a little away from the center. When the sphere is released,it oscillates. Assuming the oscillation to be simple harmonic motion and $r << R$,then the time period is

What is the velocity of the bob of a simple pendulum at its mean position,if it is able to rise to a vertical height of $10\,cm$ $(g = 9.8\,m/s^2)$?

The breaking strength of the string of a simple pendulum is twice the weight of the bob. The bob is released from rest when the string is horizontal. At what angle $\theta$ with the vertical will the string break?

Two light strings,each of length $\ell$,are fixed at points $A$ and $B$ on a fixed horizontal rod $xy$. $A$ small bob is tied by both strings and is in equilibrium,the strings are making an angle of $45^{\circ}$ with the rod. If the bob is slightly displaced normal to the plane of the strings and released,then the period of the resulting small oscillation will be: