The centre of mass of a body

Three rods of equal length $l$ are joined to form an equilateral triangle $PQR.$ $O$ is the midpoint of $PQ.$ The distance $OR$ remains the same for a small change in temperature. The coefficient of linear expansion for $PR$ and $RQ$ is the same,i.e.,$\alpha_2,$ but that for $PQ$ is $\alpha_1.$ Then the relation between $\alpha_1$ and $\alpha_2$ is:

What is the $IUPAC$ name of the following compound?

If $A = \{x \in [0, 2\pi] : \tan x - \tan^2 x > 0\}$ and $B = \{x \in [0, 2\pi] : |\sin x| < \frac{1}{2}\}$,then $A \cap B = $

An ideal refrigerator has a freezer at a temperature of $-13^{\circ}C$. The coefficient of performance of the refrigerator is $5$. The temperature of the air (to which heat is rejected) will be:

$A$ ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping.