The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10 \mathrm{~m}$. If it dissipates $10 \%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is : [Use, $\mathrm{g}: 10 \mathrm{~ms}^{-2}$ ]

A uniform rod of length $2.0 \,m$ is suspended through an end and is set into oscillation with small amplitude under gravity. The time period of oscillation is approximately .... $\sec$

Which of the following statements is not true ? In the case of a simple pendulum for small amplitudes the period of oscillation is

A simple pendulum hanging from the ceiling of a stationary lift has a time period $T_1$. When the lift moves downward with constant velocity, the time period is $T_2$, then

The bob of a simple pendulum executes simple harmonic motion in water with a period $t$, while the period of oscillation of the bob is ${t_0}$ in air. Neglecting frictional force of water and given that the density of the bob is $(4/3) ×1000 kg/m^3$. What relationship between $t$ and ${t_0}$ is true

When will the motion of a simple pendulum be simple harmonic ?