Combined Rotational and Translational Motion

A disc is spinning with an angular velocity $? \raisebox{1ex}{$\mathrm{rad}$}\!\left/ \!\raisebox{-1ex}{$\sec $}\right.$ about the axis of spin. The couple applied to the disc causing precession will be

In an automobile, if the vehicle makes a left turn, the gyroscopic torque

The rotor of a ship rotates in clockwise direction when viewed from the stern and the ship takes a left turn. The effect of the gyroscopic couple acting on it will be 

A disc spinning on its axis at $20 \raisebox{1ex}{$\mathrm{rad}$}\!\left/ \!\raisebox{-1ex}{$\sec $}\right.$ will undergo precession when a torque $100 \mathrm{N}-\mathrm{m}$ is applied about an axis normal to it at an angular speed, if mass moment of inertia of the disc is the $1 \mathrm{kg}-{\mathrm{m}}^2$-

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

A body under translational motion is rigid if:

A solid sphere of radius $r$ is gently placed on a rough horizontal surface with an initial angular speed ${\mathrm{\omega }}_0$ but no linear velocity. If the coefficient of friction is $\mathrm{\mu }$, then the time $t$ when the slipping will stop is

A spherical ball of mass $20 \mathrm{kg}$ is stationary at the top of hill of height $100 \mathrm{m}$. It rolls down a smooth surface to the ground, then climbs up another hill of height $30 \mathrm{m}$ and finally rolls down to a horizontal base at a height of $20 \mathrm{m}$ above the ground. The velocity attained by the ball is

A body rolls down an inclined plane. If its kinetic energy of rotation is $40\%$ of its kinetic energy of translation, then the body is

A round object of mass M and radius R rolls down without slipping along an inclined plane. The frictional force

A solid sphere rolls down without slipping on an inclined plane, then percentage of rotational kinetic energy of total energy will be

An object is performing uniform translatory motion. This implies:

A particle of mass$m$ moving horizontally with a velocity $v_0$ collides and sticks to the bottom of the smoothly pivoted hanging rod of mass $M (= 3 m)$and length$l$.

A uniform rod rotates in a vertical plane about the shown axis. Angular velocity at the moment is $\omega$ . Then, force on the rod by the axis at the moment

A rod of length $L$ is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the road, when it is in vertical position is

A uniform rod is hanging with the help of the unintelligible strings as shown. Then:

A wheel of radius $R$ is free to rotate about its own axis. A tangential force $F$ is applied to the wheel along its rim. If $q$ is angular displacement of the wheel due to the force $F$ then work done by $F$ is

A cord is wrapped on a pulley (disk) of mass M and radius R as shown in Figure. To one end of the cord, a block of mass M is connected as shown and to other end in (a) a force of 2 Mg and in (b) a block of mass 2M. Let angular acceleration of the disk in A and B is ${\alpha }_A$ and ${\alpha }_B$ respectively, then (cord is not slipping on the pulley)

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down(no rolling) the plane. Then maximum acceleration down the plane is for

For a rigid body made of total $\mathrm{N}$ particles each of mass $\mathrm{m}$ , the radius of gyration about a given axis equals to -