$A$ $U$-tube of uniform bore of cross-sectional area $A$ has been set up vertically with open ends facing up. Now $M$ grams of a liquid of density $d$ is poured into it. The column of liquid in this tube will oscillate with a period $T$ such that

$A$ $U$-tube of uniform bore of cross-sectional area '$A$' is set up vertically. '$M$' grams of a liquid of density '$d$' is poured into it. The column of liquid in this tube will oscillate with a period '$T$', which is equal to [$g$ = acceleration due to gravity]

$A$ disc of radius $R$ is made to oscillate about a horizontal axis passing through its periphery. Its time period would be

$A$ cylindrical piston of mass $M$ slides smoothly inside a long cylinder closed at one end,enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position,it oscillates simple harmonically. The period of oscillation will be

Two light identical springs of spring constant $k$ are attached horizontally at the two ends of a uniform horizontal rod $AB$ of length $l$ and mass $m$. The rod is pivoted at its centre $O$ and can rotate freely in a horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in the figure. The rod is gently pushed through a small angle $\theta$ and released. The frequency of the resulting oscillation is

$A$ pendulum is formed by pivoting a disc. What distance from the center of mass should it be pivoted for the minimum time period while performing $SHM$?