A thin uniform rod of length $2\,m$. cross sectional area ' $A$ ' and density ' $d$ ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$. If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha E}{ Ad }}$ then the value of $\alpha$ is $...........$

When a body is rolling without slipping on a rough horizontal surface, the work done by friction is ........

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed $v$. The sphere and the cylinder reaches upto maximum heights $h_1$ and $h_2$, respectively, above the initial level. The ratio $h_1: h_2$ is $\frac{n}{10}$. The value of $\mathrm{n}$ is__________.

A flywheel of moment of inertia $0.32\ kg-m^2$ is rotated steadily at $120\,rad/\sec $ by a $50\,W$ electric motor. The kinetic energy of the flywheel is.......... $J$

The speed of rolling of a ring of mass $M$ changes from $V$to $3\ V$. What is the change in its kinetic energy

A solid sphere rolls down without slipping on an inclined plane, then percentage of rotational kinetic energy of total energy will be ........ $\%.$