Rolling Motion

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:

These questions consists of two statements each printed as Assertion and Reason. While answering these questions you are required to choose any one of the following five responses.

Assertion: A solid sphere cannot roll without slipping on smooth horizontal surface.

Reason: If the sphere is left free on smooth inclined surface, it cannot roll without slipping.

A uniform solid cylindrical roller of mass $m$ is being pulled on horizontal surface with force $F$ parallel to the surface applied at its centre. If the acceleration of the cylinder is $a$ and it is rolling without slipping, then the value of $F$ is

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

A uniform solid ball of mass '$m$' rolls without sliding on a fixed horizontal surface. The velocity of the lowest point of the ball with respect to the center of the ball is $v$. The total kinetic energy of the ball is:

A fly wheel is in the form of a uniform circular disc of radius $1 \mathrm{m}$ and mass $2 \mathrm{kg}$. The work which must be done on it to increase its frequency of rotation from $5 \mathrm{rev} {\mathrm{s}}^{-1}$ to $10 \mathrm{rev} {\mathrm{s}}^{-1}$ is approximately

A wheel is rotating freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is $I$ and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia $3I$ initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

A ring of radius $3a$ is fixed rigidly on a table. A small ring whose mass is $m$ and radius $a$ rolls without slipping inside it as shown in the figure. The small ring is released from position $A$. When it reaches the lowest point, the speed of the centre of the ring at that time would be,

Roll the marble from different heights. Observe the effect on its movements.
Change the level of the slant of the book. Hold one end of the book with your hand and the other should touch the floor. Now, roll the marble from the end which is high to the plain floor. Mark with chalk, the place where the marble reaches. Conduct the same experiment by Changing the slope of the book each time.
Is there a relation between the slope of the book and the distance covered by the marble? 
 

Roll the marble from different heights. Observe the effect on its movements.
Change the level of the slant of the book. Hold one end of the book with your hand and the other should touch the floor. Now, roll the marble from the end which is high to the plain floor. Mark with chalk, the place where the marble reaches. Conduct the same experiment by Changing the slope of the book each time.
The marble rolled at what height covers the longest distance?

Roll the marble from different heights. Observe the effect on its movements.
Change the level of the slant of the book. Hold one end of the book with your hand and the other should touch the floor. Now, roll the marble from the end which is high to the plain floor. Mark with chalk, the place where the marble reaches. Conduct the same experiment by Changing the slope of the book each time.
The marble rolled at what height covers the shortest distance?

A flywheel is in the form of a uniform circular disc of radius $1 \mathrm{m}$ and mass $2 \mathrm{kg}$. The work which must be done on it to increase its frequency of rotation from $5 \mathrm{rev} {\mathrm{s}}^{-1}$ to $10 \mathrm{rev} {\mathrm{s}}^{-1}$ is approximately

In rotational motion of a rigid body, all particles move with _____.

A solid cylinder rolls without slipping down an inclined plane at an angle $60°$ with the horizontal. The acceleration of the cylinder is

Prove the result that the velocity $v$ of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height $h$ is given by, $v^2=2gh/(1+k^2/R^2)$ using dynamical consideration (i.e., by consideration of forces and torques). Note k is the radius of gyration of the body.

What is the ratio of total kinetic energy and translation kinetic energy of rolling body of radius $\mathrm{R}$ and radius of gyration $\mathrm{k}$?

A ring of radius $3a$ is fixed rigidly on a table. A small ring whose mass is $m$ and radius $a$, rolls without slipping inside it as shown in the figure. The small ring is released from position $A$. When it reaches the lowest point, the speed of the centre of the ring at that time would be

Give one example of the following.

Curvilinear