Embibe Experts Solutions for Chapter: Motion of System of Particles and Rigid Body, Exercise 3: Level 3

A disk of mass $M$ and radius $R$ is rolling with angular speed $\omega$ on a horizontal plane as shown. The magnitude of angular momentum of the disk about the origin $O$ is,

A sphere rolls without slipping on a rough horizontal surface with centre of mass having constant speed $v_0$. If mass of the sphere is $m$ and its radius is $R$, then what is the angular momentum of the sphere about the point of contact?

Two objects of masses $200 \mathrm{gm}$ and $500 \mathrm{gm}$ possess velocities $10î$ and $\left(3\hat{\mathit{i}}+5\hat{j}\right) \mathrm{m} {\mathrm{s}}^{-1}$, respectively. The velocity of their centres of masses in $\mathrm{m} {\mathrm{s}}^{-1}$ is

Three particles of masses $1 \mathrm{kg}$, $2 \mathrm{kg}$ and $3 \mathrm{kg}$ are subjected to forces $\left(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}+2\hat{\mathrm{k}}\right) \mathrm{N}$, $\left(-\hat{\mathrm{i}} +2\hat{\mathrm{j}} -\hat{\mathrm{k}}\right) \mathrm{N}$ and $\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\right) \mathrm{N}$, respectively. The magnitude of the acceleration of the COM of the system is

Two bodies of mass $10 \mathrm{kg}$ and $2 \mathrm{kg}$ are moving with velocity $\left(2\hat{\mathrm{i}}-7\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right) \mathrm{m} {\mathrm{s}}^{-1}$ and $\left(-10\hat{\mathrm{i}}+35\hat{\mathrm{j}}-3\hat{\mathrm{k}}\right) \mathrm{m} {\mathrm{s}}^{-1}$, respectively. The velocity of their centre of mass is

A circular turntable has a block of ice placed at its centre. The system rotates with an angular speed $\text{ω}$ about an axis passing through the centre of the table. If the ice melts on its own without any evaporation, the speed of rotation of the system,

An ant is sitting at the edge of a rotating disk. If the ant reaches the other end after moving along the diameter, the angular velocity of the disk will,

A body is moving around the sun in an elliptical orbit. The maximum and minimum distance are $3\times {10}^{12} \mathrm{m}$and $2\times {10}^{10} \mathrm{m}$. The velocity at a minimum distance is$2\times {10}^7 \mathrm{m} {\mathrm{s}}^{-1}$. Find the velocity of the body at maximum distance.