A rail track made of steel having length $10\,m$ is clamped on a railway line at its two ends as shown in figure. On a summer day due to rise in temperature by $20\,^oC$ , it is deformed as shown in figure. Find $x$ (displacement of the centre) if  $\alpha _{steel} = 1.2 \times 10^{-5} \,^oC^{-1}$

If the length of the pendulum in pendulum clock increases by $0.1\, \%$, then the error in time per day is: (in $s$)

A gas follows $VT^2 =$ constant. The coefficient of volume expansion of the gas is

Suppose there is a hole in a copper plate. On heating the plate, diameter of hole, would

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