The relation between the coefficient of real expansion $(\gamma_r)$ and coefficient of apparent expansion $(\gamma_a)$ of a liquid and the coefficient of linear expansion $(\alpha_g)$ of the material of the container is

Two blocks of masses $1 ~kg$ and $2 ~kg$ are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is $2 \times 10^9 ~N/m^2$. What should be the minimum radius of the wire used if it is not to break? Take $g = 10 ~m/s^2$.

Which of the following is the characteristic outer electronic configuration of alkaline earth metals?

Three moles of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperatures in different states are: $T_1 = 400\, K, T_2 = 800\, K, T_3 = 2400\, K$ and $T_4 = 1200\, K$. The work done by the gas during the cycle is .... $kJ$.

$A$ simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. $A$ small peg is placed at a distance $2L/3$ directly below the fixed pivot point. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?

If $\sin A + \sin B = \sqrt{3}(\cos B - \cos A)$,then $\sin 3A + \sin 3B$ is equal to: