A one litre glass flask contains some mercury. It is found that at different temperatures the volume of air inside the flak remains the same. ...... $cc$ is the volume of mercury in this flask if coefficient of linear expansion of glass is $9 \times 10^{-6} /^o C$ while of volume expansion of mercury is $1.8 \times {10^4}\,/^\circ C$
$50$
$100$
$150$
$200$
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)
A beaker of height $H$ is made up of a material whose coefficient of linear thermal expansion is $3\alpha $ . It is filled up to the brim by a liquid whose coefficient of thermal expansion is $\alpha $. If now the beaker along with its contents is uniformly heated through a small temperature $T$ the level of liquid will reduce by (given $\alpha << 1$)
The density of water at $20^oC$ is $0.998\ gm/cm^3$ and at $40^oC$ is $0.992\ gm/cm^3$. The mean coefficient of cubical expansion (in per ${}^oC$) is
A rod of length $10\ meter$ at $0\,^oC$ having expansion coefficient $\alpha = (2x^2 + 1) \times 10^{-6}\,C^{-1}$ where $x$ is the distance from one end of rod. The length of rod at $10\,^oC$ is
An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The diameter of tyre is $6\, mm$ smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of ........ $^oC$ (the coefficient of cubical expansion of iron is ${3.6 \times 10^{-5} } °C^{-1}$)