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 ..... $\sec$

There is a simple pendulum hanging from the ceiling of a lift. When the lift is stand still, the time period of the pendulum is $T$. If the resultant acceleration becomes $g/4,$ then the new time period of the pendulum is

A simple pendulum is taken from the equator to the pole. Its period

Two pendulums begin to swing simultaneously. If the ratio of the frequency of oscillations of the two is $7 : 8$, then the ratio of lengths of the two pendulums will be

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

A simple pendulum is released from rest at the horizontally stretched position. When the string makes an angle $\theta$ with the vertical, the angle $\phi$ which the acceleration vector of the bob makes with the string is given by