$A$ solid sphere of mass $1 \ kg$ is rolling on a rough table with a linear speed of $1 \ m/s$. Its total kinetic energy is ....... $J$.

$A$ ring and a disc roll on a horizontal surface without slipping with the same linear velocity. If both have the same mass and the total kinetic energy of the ring is $6 \ J$,then the total kinetic energy of the disc is: (in $/2 \ J$)

$A$ small roller of diameter $20 \ cm$ has an axle of diameter $10 \ cm$. It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle. The scale is now pushed slowly on the axle so that it moves without slipping on the axle,and the roller starts rolling without slipping. After the roller has moved $50 \ cm$,the position of the scale will look like (figures are schematic and not drawn to scale)-

Consider a point $P$ at the contact point of a wheel on the ground,which rolls on the ground without slipping. Find the displacement of point $P$ when the wheel completes half of a rotation (given the radius of the wheel is $1 \ m$).

$A$ solid sphere of mass $2\,kg$ is making pure rolling on a horizontal surface with kinetic energy $2240\,J$. The velocity of the centre of mass of the sphere will be $..........\,m/s$.

$A$ wheel of radius $r$ is rolling on a straight line,with the velocity of its centre being $v$. At a certain instant,the point of contact of the wheel with the ground is $M$ and $N$ is the highest point on the wheel (diametrically opposite to $M$). Which of the following statements is incorrect?