Subject Experts Solutions for Chapter: Centre of Mass and Rotational Motion, Exercise 1: Practice Exercise

A sphere rolls down on an inclined plane of inclination $\theta$. What is the acceleration as the sphere reaches bottom

One circular ring and one circular disc, both are having the same mass and radius. The ratio of their moment of inertia about the axis passing through their centres and perpendicular to their planes, will be

A thin wire of length $l$ and mass $m$ is bent in the form of a semicircle. Its moment of inertia about an axis joining its free ends will be

Three masses are placed on the $X$-axis, $300 \mathrm{g}$ at origin, $500 \mathrm{g}$ at $x=40 \mathrm{cm}$ and $400 \mathrm{g}$ at $x=70 \mathrm{cm}$. The distance of centre of mass from the origin is

A sphere of mass $10 \mathrm{kg}$ and radius $0.5 \mathrm{m}$ rotates about a tangent. The moment of inertia of the solid sphere is

A wheel of mass $10 \mathrm{kg}$ has moment of inertia $160 \mathrm{kg} {\mathrm{m}}^2$ about its own axis. The radius of gyration will be,

Consider a two particles system with particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass through a distance $d$, by what distance should the second particle be moved so as to keep the centre of mass at the same position?

A particle of mass $2 \mathrm{kg}$ is moving such that at a time $t$, its position in metre is given by, $r\left(t\right)=5\hat{\mathrm{i}}-2t^2\hat{\mathrm{j}}$. The angular momentum of the particle at $t=2 \mathrm{s}$ about the origin in $\mathrm{kg} {\mathrm{m}}^{-2} {\mathrm{s}}^{-1}$ is,