$A$ sphere of mass $0.5 \ kg$ and diameter $1 \ m$ is rolling without slipping with a constant velocity of $5 \ m/s$. The ratio of its rotational kinetic energy to its total kinetic energy is:

$A$ disc of radius $1\,m$ and mass $4\,kg$ rolls on a horizontal plane without slipping in such a way that its centre of mass moves with a speed of $10\,cm/s$. Its rotational kinetic energy is (in $,J$)

$A$ sphere of mass $50\,g$ and diameter $20\,cm$ rolls without slipping with a velocity of $5\,cm/s$. Its total kinetic energy is

$A$ solid sphere of mass $1\,kg$ rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3}\,J$. The speed of the centre of mass of the sphere is $.........\,cm\,s^{-1}$.

$A$ 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?

At time $t=0$,a disk of radius $1 \text{ m}$ starts to roll without slipping on a horizontal plane with an angular acceleration of $\alpha = \frac{2}{3} \text{ rad s}^{-2}$. $A$ small stone is stuck to the disk. At $t=0$,it is at the contact point of the disk and the plane. Later,at time $t=\sqrt{\pi} \text{ s}$,the stone detaches itself and flies off tangentially from the disk. The maximum height (in $\text{m}$) reached by the stone measured from the plane is $\frac{1}{2} + \frac{x}{10}$. The value of $x$ is. . . . . . . [Take $g=10 \text{ m s}^{-2}$.]