Rigid Body

A string is wrapped over a uniform cylinder, as shown in diagram. When cylinder is released, string unwraps without any slipping and cylinder comes down. Which of the following is true?

A cylinder is moving along a horizontal surface without slipping with an angular velocity $\omega =1.0 \mathrm{rad}/\mathrm{s}.$ If the rod is leaning on the cylinder with one end hinged. Then which of the following statements is/are correct for the moment when angle $\alpha =60°?$

A uniform rod of length $4 \mathrm{m}$ and mass $2\sqrt{2} \mathrm{kg}$ revolves with constant angular velocity $\omega$ about a vertical axis through a smooth joint A at one extremity of the rod so that it describes a cone of semi vertical angle $53°$ as shown in the figure. choose the INCORRECT statement(s). $\left(g=10 \mathrm{m} {\mathrm{s}}^{-1}\right)$

A cylinder $P$ of radius $r_P$ is being rotated at a constant angular velocity ${\omega }_P\hat{j}$ with the help of a motor about its axis that is fixed. Another cylinder $Q$ of radius $r_Q$ free to rotate about its axis that is also fixed is touched with the pressed on P making angle $\theta$ between their axes. Soon after the cylinders are pressed against each other, a steady state is reached and the cylinder $Q$ acquires a constant angular velocity. What can you conclude when the steady state is reached?

A disc placed on a frictionless horizontal plank is rotating with a constant angular velocity $\omega$ about its central vertical axis. Now the plank is made to move with a constant acceleration $\alpha$ on a straight path. If you assume initial location of the centre of disc as origin, direction of motion of the plank in negative $y$-axis of the coordinate system attached with the plank, which of the following equations represent trajectroy of instantaneous centre of rotation of the disc.

A disc of mass $m$ and radius $R$ is placed over a plank of mass $m$. There is sufficient friction between disc and plank to prevent slipping and there is no friction between plank and ground. A horizontal force $F$ is applied at the centre of the disc, then

A sleeve $A$ can slide freely along a smooth rod bent in the shape of a half-circle of radius $R$ (Fig.). The system is set in rotation with a constant angular velocity $\omega$ about a vertical axis $OO$'. The angle corresponding to the equilibrium position of the sleeve is given by $\theta$. Then

A hemispherical bowl of radius $R=0.2 \mathrm{m}$ is rotating about its own axis vertically with an angular frequency $\omega$. A particle of mass $0.02 \mathrm{kg}$ on the frictionless inner surface of the bowl is also rotating with the same frequency $\omega$. The particle is at a height $h$ from the bottom of the bowl. Which of the following statement(s) is/are true? (Take, the least count in the measurement of $h$ is ${10}^{-3} \mathrm{m}$)

A double star is a system of two stars rotating about their centre of mass only under their mutual gravitational attraction. Let the stars have masses $m$ and $2 \mathrm{m}$and let their separation be $l$. Their time period of rotation about their centre of mass will be proportional to

Rotation of the lever $OA$ is controlled by the motion of the contacting circular disk whose centre is given a horizontal velocity $v$. Determine the expression of the angular velocity of the lever $OA$ in terms of $x$.

A solid body rotates about a stationary axis so that its angular velocity depends upon the rotation angle $\theta$ as $\omega ={\omega }_0-k\theta$, where ${\omega }_0$ and $\theta$ are positive constants. At the moment $t=0$, the angle $\theta =0$. Which of the following variations are correct?

The angular velocity $\left(\omega \right)$ and the angular acceleration $\left(\alpha \right)$ are plotted with time as shown. Which of the following options are incorrect?

Consider a bob of mass $m$ and having charge $q$ attached with a light string of length $l$ and pivoted at point $O$. It is released at rest at $60°$ with vertical. There are two regions - Region-I (left of line $PQ$) has a uniform and constant magnetic field $B$ directed inside plane of paper. Region-II (right of line $PQ$) has a constant and uniform electric field $E$ directed vertically up as shown. Consider no effect of gravity in both the regions.

A small object is placed on a smooth table at a distance $r_0$ from a hole in the centre of table. An ideal inextensible chord is attached to the object through this hole. The object is set into motion with initial velocity of magnitude ${\mathrm{v}}_0$ at right angle to the chord and at the same time, the chord is pulled through the hole at uniform speed $\mathrm{cm} {\mathrm{s}}^{-1}$. Initially object is at point $A\left(0,r_0\right)$ and at any time $t$, it is at point $P\left(r\cos \theta ,r\sin \theta \right).$ Neglect the dimension of object. Choose CORRECT option (s).

A uniform disc is performing pure rolling on a smooth horizontal stationary surface with constant angular velocity ($V/R$) and linear velocity of centre of mass $V$ as shown is fig. find the correct statements at the given instant of time (Radius of the disc is $R$) (Assume $A,B,C,D$ are on the circumference of the disc.)

A thin uniform bar lies on a frictionless surface and is free to move in any way on the surface. Its mass is $0.16 \mathrm{kg}$ and length $\sqrt{3}$ metres. Two particles each of mass $0.08 \mathrm{kg}$ are moving on the same surface and towards the bar in a direction perpendicular to the bar, one with a velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$ and the other with $6 \mathrm{m} {\mathrm{s}}^{-1}$ as shown in Figure. The first particle strikes the bar at $A$ and the other at the point $B$. The points $A$ and $B$ are at distance $0.5 \mathrm{m}$ from centre of the bar. The particle strike the bar at the same instant of time and stick to the bar on collision. Calculate the loss of kinetic energy of the system in the above collision process.

A uniform solid cylinder of radius $R=15 \mathrm{cm}$ rolls over a horizontal plane passing in to an inclined plane forming an angle $\alpha =30°$ with the horizontal. Find the maximum value of the velocity $v_0$ which still permits the cylinder to roll onto the inclined plane section without a jump. The sliding is assumed to be absent.

Which one of the following motion include translational motion of the rigid body?

What do you mean by the translational motion of a rigid body?

A body under translational motion is rigid if: