$A$ 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 $s$)

$A$ 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):

One end of a $V$-tube containing mercury is connected to a suction pump and the other end to the atmosphere. The two arms of the tube are inclined to the horizontal at an angle of $45^{\circ}$ each. $A$ small pressure difference is created between the two columns when the suction pump is removed. Will the column of mercury in the $V$-tube execute simple harmonic motion? Neglect capillary and viscous forces. Find the time period of oscillation.

$A$ particle of mass $m$ is executing oscillations about the origin on the $x-$axis. Its potential energy is $V(x) = k | x |^3$,where $k$ is a positive constant. If the amplitude of oscillation is $a$,then its time period $T$ is

$A$ small spherical ball of radius '$r$' is rolling on a curved surface which is frictionless and has a radius of curvature '$R$'. Its motion is simple harmonic. Then its time period of oscillation is proportional to ($g=$ acceleration due to gravity).

$A$ long stiff uniform wire of length $\ell$ is suspended from one end. The time period of oscillations of the wire is $T$. If the wire is now bent into a circle and suspended from a knife edge so that it can oscillate freely in the plane of the ring,its time period will be