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

$A$ sound wave passing through an ideal gas at $NTP$ produces a pressure change of $0.001 \text{ dyne}/cm^2$ during adiabatic compression. The corresponding change in temperature $(\gamma = 1.5$ for the gas and atmospheric pressure is $1.013 \times 10^6 \text{ dyne}/cm^2)$ is:

$A$ uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. $A$ horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of the face,at a height $\frac{3a}{4}$ above the base. The minimum value of $F$ for which the cube begins to tilt about the edge is (Assume that the cube does not slide):

The resistance of a wire is $R$. It is bent at the middle by $180^{\circ}$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is

The equation $\sqrt{3} \sin x + \cos x = 4$ has

The extension in a string,obeying Hooke's law,is $x$. The speed of sound in the stretched string is $v$. If the extension in the string is increased to $1.5x$,the speed of sound will be (in $, v$)