$A$ 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

$A$ small sphere oscillates simple harmonically in a watch glass whose radius of curvature is $1.6 \ m$. The period of oscillation of the sphere is (acceleration due to gravity $g = 10 \ m/s^2$) (in $\pi \ s$)

Two pendulums differ in lengths by $22 \ cm$. They oscillate at the same place such that one of them makes $15 \ oscillations$ and the other makes $18 \ oscillations$ during the same time. The lengths (in $cm$) of the pendulums are

In an elevator,a spring clock of time period $T_S$ (mass attached to a spring) and a pendulum clock of time period $T_P$ are kept. If the elevator accelerates upwards,what happens to their time periods?

$A$ simple pendulum, consisting of a small ball of mass $m$ attached to a massless string hanging vertically from the ceiling, is oscillating with an amplitude such that $T_{\max } = 2 T_{\min }$, where $T_{\max }$ and $T_{\min }$ are the maximum and minimum tension in the string respectively. The value of maximum tension $T_{\max }$ in the string is

$A$ wooden cube (density of wood $d$) of side $l$ floats in a liquid of density $\rho$ with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released,it performs simple harmonic motion of period $T$. Then,$T$ is equal to