A disc of radius $\mathrm{R}=10\mathrm{ }\mathrm{c}\mathrm{m}$ oscillates as a physical pendulum about an axis perpendicular to the plane of the disc at a distance $\mathrm{r}$ from its centre. Consider a distance $\mathrm{r}=\frac{\mathrm{R}}{4}$ from the centre. What is the approximate period of oscillation ?
(Take $\mathrm{ }\mathrm{g}=10\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$ )

The position co-ordinates of a particle moving in a $3D$ coordinate system is given by

$x=a\cos \mathrm{\omega }\mathrm{t}$

$y=a\sin \omega t$

and $z=a\omega t$

The speed of the particle is:

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $\mathit{\text{M}}$. The piston and the cylinder have equal cross-sectional area $\mathit{\text{A}}$. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $M_0$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[Assume the system is in space.]

A source of sound emits sound waves at frequency $f_0$ . It is moving towards an observer with fixed speed $v_s (v_s<\mathrm{v)}$ , where $v$ is the speed of sound in air). If the observer were to move towards the source with speed $v_0$ , one of the following two graphs (A and B) will give the correct variation of the frequency $f$ heard by the observer as $v_0$ is changed.



The variation of $f$ with $v_0$ is given correctly by: