$A$ test tube of mass $6 \ g$ and uniform area of cross-section $10 \ cm^2$ is floating in water vertically when $10 \ g$ of mercury is in the bottom. The tube is depressed by a small amount and then released. The time period of oscillation is (Acceleration due to gravity $= 10 \ m/s^2$) (in $s$)

$A$ body of mass $m$ is situated in a potential field $U(x) = U_0 (1 - \cos \alpha x)$,where $U_0$ and $\alpha$ are constants. Find the time period of small oscillations.

$A$ particle of mass $4 \,kg$ moves simple harmonically such that its potential energy $U$ varies with position $x$ as shown in the figure. The period of oscillations is ............

$A$ drinking straw is dipped in a pan of water to a depth $d$ from the surface (see figure). Water is sucked into it up to an initial height $h_0$ and then left to oscillate. As a result,its height $y$ from the surface of the water varies periodically. Ignoring damping,the equation for $y$ is ($g$ is the acceleration due to gravity):

$A$ sphere of radius $r$ is kept on a concave mirror of radius of curvature $R$. The arrangement is kept on a horizontal table (the surface of the concave mirror is frictionless and the sphere is sliding,not rolling). If the sphere is displaced from its equilibrium position and released,it executes $S.H.M.$ The period of oscillation will be

$A$ number of holes are drilled along a diameter of a disc of radius $R$. To get the minimum time period of oscillations,the disc should be suspended from a horizontal axis passing through a hole whose distance from the centre should be: