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

On a planet a freely falling body takes $2 \,sec$ when it is dropped from a height of $8 \,m$, the time period of simple pendulum of length $1\, m$ on that planet is ….. $\sec$

In a seconds pendulum, mass of bob is $30\, g$. If it is replaced by $90\, g$ mass. Then its time period will be … $\sec$

A pendulum has time period $T$. If it is taken on to another planet having acceleration due to gravity half and mass $ 9 $ times that of the earth then its time period on the other planet will be

The periodic time of a simple pendulum of length $1\, m $ and amplitude $2 \,cm $ is $5\, seconds$. If the amplitude is made $4\, cm$, its periodic time in seconds will be