The displacement $y(t) = A\,\sin \,(\omega t + \phi )$ of a pendulum for $\phi = \frac {2\pi }{3}$ is correctly represented by

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 ..... $\sec$

The length of a seconds pendulum at a height $h=2 R$ from earth surface will be.(Given: $R =$ Radius of earth and acceleration due to gravity at the surface of earth $g =\pi^{2}\,m / s ^{-2}$ )

A simple pendulum consisting of a ball of mass $m$ tied to a thread of length $l$ is made to swing on a circular arc of angle $\theta $ in a vertical plane. At the end of this arc, another ball of mass $m$ is placed at rest. The momentum transferred to this ball at rest by the swinging ball is

A simple pendulum has time period 't'. Its time period in a lift which is moving upwards with acceleration $3 ms ^{-2}$ is

The acceleration due to gravity on the surface of moon is $1.7 \;ms ^{-2}$. What is the time period of a simple pendulum on the surface of moon if its time period (in $sec$) on the surface of earth is $3.5\; s ?( g$ on the surface of earth is $9.8\; ms ^{-2} )$