If a solid sphere of mass $1\, kg$ and radius $0.1\, m$ rolls without slipping at a uniform velocity of $1\, m/s$ along a straight line on a horizontal floor, the kinetic energy is

Two uniform circular discs are rotating independently in the same direction around their common axis passing through their centres. The moment of inertia and angular velocity of the first disc are $0.1 \;kg - m ^{2}$ and $10\; rad \,s^{-1}$ respectively while those for the second one are $0.2 \;kg - m ^{2}$ and $5\; rad \,s ^{-1}$ respectively. At some instant they get stuck together and start rotating as a single system about their common axis with some angular speed. The Kinetic energy of the combined system is ...........$J$

Two uniform similar discs roll down two inclined planes of length $S$ and $2S$ respectively as shown is the fig. The velocities of two discs at the points $A$ and $B$ of the inclined planes are related as

$A$ ring of mass $m$ is rolling without slipping with linear velocity $v$ as shown is figure. $A$ rod of identical mass is fixed along one of its diameter. The total kinetic energy of the system is :-

A disc is rolling without slipping on a straight surface. The ratio of its translational kinetic energy to its total kinetic energy is

A thin hollow cylinder open at both ends:

$(i)$ Slides without rotating

$(ii)$ Rolls without slipping, with the same speed