Rigid Bodies: Translational Motion And Rotational Motion MCQ - Practice Questions with Answers

A solid sphere and cylinder of identical radii and mass approach an incline with the same linear velocity (see figure ). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The ratio $\frac{h_{sph}}{h_{cyl}}$ is given by:

As given in the diagram two plates A and B move with velocities -V  and 3V . If the sphere does not slide relative to the plate . Assuming mass of each body as m Find the kinetic energy of sphere 

A hollow sphere rolling on a surface. what is the % of its translational kinetic energy -

A solid sphere is rolling on a surface its speed is and mass .The its Kinetic energy is__

A heavy spool with an inner radius of 10 cm ' and an outer radius ' of 20 cm ' is lying on a rough horizontal plane. A thread of negligible mass is wound over it and is being pulled with a constant force at an angle ' $\alpha$ ' from the vertical as shown in the figure. Find the angle ' $\alpha$ ' for which the centre of the spool remains at rest.

As shown in figure a particle of mass m moves in the x - y plane with a velocity v along the direction AB. $L_A$ is the angular momentum of a particle at A with respect to origin and $L_B$ when it is at B then

A spinning solid spherical ball having angular velocity $\frac{V_0}{2r}$ is projected on a horizontal rough surface with velocity $v_0$.. The velocity of centre of mass of the ball when slipping ceases, will be

Two balls of mass ${\mathrm{m}}_1=1.0\mathrm{kg}$ and $m_2=0.5\mathrm{kg}$ are suspended on two strings of length $l_1=10\mathrm{cm}$ and $l_2=20\mathrm{cm}$ at the end of a freely hanging rod.

The rod is rotating with an angular velocity of $15\mathrm{rad}/\mathrm{s}$ about the vertical axle such that it remains in the vertical position. If the tension in the strings is $T_1$ and $T_2$ respectively, then find the sum of $T_1$ and $T_2$.

A rod with linear mass density given, as - $\lambda =\frac{{\lambda }_0{x}^2}{l^2}$ where, $x$ is the distance from its left most end and ' $l$ ' is the length of the rod. If the rod is placed on a smooth horizontal plane and a force of constant magnitude $F$ is applied on its rightmost end then the angular acceleration of the rod will be.

Two hollow cylinders of radii ' $1m$ ' and ' $2m$ ' respectively have a common geometrical axis as shown in the figure.

A fly starts with a constant speed ' $v$ ' and hits the outer cylinder at ' X ' from inside. If both the cylinder starts rotating with an angular velocity of ' $1\mathrm{rad}/\mathrm{s}$ '. The fly strikes another point ' Y ' where the distance between ' $X$ ' and ' $Y$ ' is 10 cm. Assuming the fly moves radially, find the speed of the fly.