The graphs below show angular velocity $\omega$ as a function of time $t$. In which one is the magnitude of the angular acceleration $\alpha$ constantly decreasing?

The total kinetic energy of a body of mass $10 \ kg$ and radius $0.5 \ m$ moving with a velocity of $2 \ m/s$ without slipping is $32.8 \ J$. The radius of gyration of the body is .......... $m$.

$A$ $2 \, kg$ steel rod of length $0.6 \, m$ is clamped on a table vertically at its lower end and is free to rotate in a vertical plane. The upper end is pushed so that the rod falls under gravity. Ignoring the friction due to clamping at its lower end,the speed of the free end of the rod when it passes through its lowest position is $\ldots \ldots \ldots \ldots \, ms^{-1}$. (Take $g = 10 \, ms^{-2}$)

$A$ meter stick is held vertically with one end on the floor and is allowed to fall. The speed of the other end when it hits the floor,assuming that the end at the floor does not slip,is ......... $m/s$ $(g = 9.8 \, m/s^2)$.

$A$ hemisphere of mass $3m$ and radius $R$ is free to slide with its base on a smooth horizontal table. $A$ particle of mass $m$ is placed on the top of the hemisphere. If the particle is displaced with a negligible velocity,find the angular velocity of the particle relative to the centre of the hemisphere at an angular displacement $\theta$,when the velocity of the hemisphere is $v$.

Which one of the following four graphs best depicts the variation with $x$ of the moment of inertia $I$ of a uniform triangular lamina about an axis parallel to its base at a distance $x$ from it?