Two loops $P$ and $Q$ are made from a uniform wire. The radii of $P$ and $Q$ are $r_1$ and $r_2$ respectively, and their moments of inertia are $I_1$ and $I_2$ respectively. If $I_2/I_1=4$ then $\frac{{{r_2}}}{{{r_1}}}$ equals
$4^{2/3}$
$4^{1/3}$
$4^{-2/3}$
$4^{-1/3}$
An ant is sitting at the edge of a rotating disc. If the ant reaches the other end, after moving along the diameter, the angular velocity of the disc will
One end of a rod of length $L=1 \,m$ is fixed to a point on the circumference of a wheel of radius $R=1 / \sqrt{3} \,m$. The other end is sliding freely along a straight channel passing through the centre $O$ of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity $\omega$ about $O$. The speed of the sliding end $P$, when $\theta=60^{\circ}$ is
A cockroach of mass $\frac {M}{2}$ is start moving, with velocity $V$ on the circumference of a disc of mass $'M'$ and $'R',$ what will be angular velocity of disc?
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
We have two spheres one of which is hollow and the other solid. They have identical masses and moment of inertia about their respectively diameters. The ratio of their radius is given by