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

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

Give temperature $^oC$, $^oF$ and $K$ when density of water is maximum.

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 $1.8 \times {10^4}\,/^\circ C$

The coefficient of linear expansion of brass and steel are ${\alpha _1}$ and ${\alpha _2}$. If we take a brass rod of length ${l_1}$ and steel rod of length ${l_2}$ at $0°C$, their difference in length $({l_2} - {l_1})$ will remain the same at a temperature if

A uniform cylindrical rod of length $L$ and radius $r$, is made from a material whose Young's modulus of Elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to

Two rods, one of aluminum and the other made of steel, having initial length ${l_1}$ and ${l_2}$ are connected together to form a single rod of length ${l_1} + {l_2}$. The coefficients of linear expansion for aluminum and steel are ${\alpha _a}$ and ${\alpha _s}$ respectively. If the length of each rod increases by the same amount when their temperature are raised by ${t^o}C$, then find the ratio $\frac{{{l_1}}}{{({l_1} + {l_2})}}$