The ratio of frequencies of two oscillating pendulums are $3: 2$. Their lengths are in the ratio:

$A$ pendulum bob has a speed of $3\, m/s$ at its lowest position. The pendulum is $0.5\, m$ long. The speed of the bob,when the length makes an angle of $60^o$ with the vertical,will be ..... $m/s$ (If $g = 10\, m/s^2$)

$A$ 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

The length of a simple pendulum is increased by $1\%$. Its time period will

The angular velocity and the amplitude of a simple pendulum are $\omega$ and $A$ respectively. At a displacement $x$ from the mean position,its kinetic energy is $T$ and potential energy is $V$. Then the ratio $\frac{V}{T}$ is

$A$ simple pendulum of length $1 \,m$ is freely suspended from the ceiling of an elevator. The time period of small oscillations as the elevator moves up with an acceleration of $2 \,m/s^2$ is (use $g=10 \,m/s^2$).