Embibe Experts Solutions for Exercise 4: Assignment

A uniform disc of mass $\mathrm{M}$ and radius $R$ is suspended in vertical plane from a point on its periphery. Its time period of oscillation is

A solid cylinder of density ${\rho }_0$, cross-section area $A$ and length $l$ floats in a liquid of density $\rho \left(>{\rho }_0\right)$ with its axis vertical, as shown. If it is slightly displaced downward and released, the time period will be

A block of mass $m$ hangs from three springs having same spring constant $k.$ If the mass is slightly displaced downwards, the time period of oscillation will be

An assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. At this instant, the springs are relaxed. The left mass is displaced to the left and the right mass is displaced to the right by same distance and released. The resulting collision is elastic. The time period of the oscillations of system is

A block of mass $\mathrm{m}$ is suspended separately by two different springs have time period $t_1$ and $t_2$. If same mass is connected to parallel combination of both springs, then its time period is given by

The potential energy of a particle of mass $100 \mathrm{g}$ moving along $x-$axis is given by $U=5 x(x-4),$ where $x$ is in metre. The period of oscillation is

A uniform thin ring of radius $R$ and mass $m$ suspended in a vertical plane from a point in its circumference. Its time period of oscillation is

Imagine a narrow tunnel between the two diametrically opposite points of the earth. A particle of mass $m$ is released in this tunnel. The time period of oscillation is