The scale on a steel metre stick is calibrated at $20^o\,C$.The error in the reading of $50\,cm$ at $30^o\,C$ is: (take linear expansion coefficient of steel $= 1.0 \times 10^{-5} /  ^oC)$

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

Two rods $A$ and $B$ of identical dimensions are at temperature $30\,^oC$. If a heated upto $180\,^oC$ and $B$ upto $T\,^oC$, then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4:3$, then the value of $T$ is........$^oC$

Water falls from a height $500m$. What is the rise in temperature of water at bottom if whole energy remains in the water ........... $^\circ \mathrm{C}$

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 $\frac{{{l_1}}}{{({l_1} + {l_2})}}$

Give value of coefficient of volume expansion at room temperature for ideal gas.