A uniform solid sphere of mass $m$ and radius $r$ rolls without slipping down a inclined plane, inclined at an angle $45^o$ to the horizontal. Find the magnitude of frictional coefficient at which slipping is absent
$\frac{1}{3}$
$\frac{2}{7}$
$\frac{1}{5}$
$\frac{1}{7}$
The centre of mass of a body
A tube of length $L$ is filled completely with incompressible liquid of mass $M$ and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega $. The force exerted by the liquid on the tube at other end is
The centre of mass of a body
$ ABC$ is a triangular plate of uniform thickness. The sides are in the ratio shown in the figure. $I_{AB}, I_{BC}, I_{CA}$ are the moment of inertia of the plate about $AB, BC$ and $CA$ respectively. Which one of the following relations is correct