If the earth were to suddenly contract to $\frac{1}{n}^{th}$ of its present radius without any change in its mass then duration of the new day will be

Five masses each of $2\, kg$ are placed on a horizontal circular disc, which can be rotated about a vertical axis passing through its centre and all the masses be equidistant from the axis and at a distance of $10\, cm$ from it. The moment of inertia of the whole system (in $gm-cm^2$) is (Assume disc is of negligible mass)

The plank in the figure moves a distance $100\,mm$ to the right while the centre of mass of the sphere of radius $150\, mm$ moves a distance $75\,mm$ to the left. The angular displacement of the sphere (in radian) is  (there is no slipping anywhere) :-

A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\, J$. ........ $J$ is its translational $K.E.$

A uniform rod of mass $m$ and length $l$ rotates in a horizontal plane with an angular velocity $\omega $ about a vertical axis passing through one end. The tension in the rod at a distance $x$ from the axis is

When a uniform solid sphere and a disc of the same mass and of the same radius rolls down a rough inclined plane from rest to the same distance, then the ratio of the time taken by them is