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

The mass per unit length of a rod of length $l$ is given by : $\lambda = \frac{M_0x}{l}$ ,where $M_0$ is a constant and $x$ is the distance from one end of the rod. The position of  centre of mass of the rod is

Ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively then ratio of moment of inertia will be

A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega $. Its centre of mass rises to a maximum height of:

$ 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