The weight of sphere in air is $50\ g$. Its weight $40\  g$ in a liquid, at temperature $20\,^o C$. When  temperature increases to $70\,^o C$ , it weight becomes $45\  g$, then the ratio of densities of liquid at given two temperature is

Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be

( ${\alpha _1},\,{\alpha _2},$ = linear expansion coefficient

$A_1, A_2$ = Area of rods

$Y_1, Y_2$ = Young modulus)

The volume of a gas at $20°C$ is $100 \,cm^3$ at normal pressure. If it is heated to $100°C$, its volume becomes $125\, cm^3$ at the same pressure, then volume coefficient of the gas at normal pressure is

A rod is placed on a smooth horizontal surface. The stress developed when temperature is increased by $40\,^oC$

$[\alpha = 5\, \times\, 10^{-5}\,^oC^{-1},\,\, \gamma = 5\, \times\, 10^{11}\,\, N/m^2]$

A hole is drilled in a metal sheet. At $27^{\circ}\,C$, the diameter of hole is $5\,cm$. When the sheet is heated to $177^{\circ}\,C$, the change in the diameter of hole is $d \times$ $10^{-3}\,cm$. The value of $d$ will be $...........$ if coefficient of linear expansion of the metal is $1.6 \times$ $10^{-5} /{ }^{\circ}\,C$

Coefficient of real expansion of mercury is $ 0.18 \times 10^{-3}{°C^{-1}}$. If the density of mercury at $0°C$ is $13.6\, gm/cc$. its density at $473K$ is