Translation and Rotation of a Body

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:

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

A cyclist riding the bicycle at a speed of $14\sqrt{3} \mathrm{m} {\mathrm{s}}^{-1}$ takes a turn around a circular road of radius  $20\sqrt{3} \mathrm{m}$ without skidding. Given $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$, what is his inclination to the vertical.

For the rigid body executing pure rotational motion, the angular velocity of all the particles is same.

Define rotational motion of rigid body.

A $\mathrm{T}$ shaped object with dimensions shown in the figure is lying on a smooth floor. A force $\overrightarrow{\mathrm{F}}$ is applied at the point $P$ parallel to $AB$, such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$.

Show that the angle of banking is independent of mass of vehicle.

Give one example of the following.

Curvilinear

A disc of radius $R$ is rotating with an angular velocity ${\omega }_0$ about a horizontal axis. It is placed on a horizontal table. The coefficient of kinetic friction is ${\mu }_{\mathrm{k}}$. What condition should be satisfied for the rolling to begin?

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 road of width $20 \mathrm{m}$ forms an arc of radius $15 \mathrm{m}$, its outer edge is $2 \mathrm{m}$ higher than its inner edge. Calculate for what velocity the road is banked

A cyclist goes round a circular path of length 400 m in 20 s. calculate the angle through which he bends from vertical in order to maintain the balance

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 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 -

A car is moving on an unbanked circular bend of radius $50\mathrm{ }\mathrm{m}$, at a speed of $36\mathrm{ }\mathrm{k}\mathrm{m} {\mathrm{hr}}^{-1}$. The angle of banking required for the safe turning of the car is (Take $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$.)

Select the wrong statement -

Statement-I : A body may be in pure rotation under the action of single external force.

Statement-II : If a body is in pure rotation under action of single external force then it must not be rigid.