A pendulum clock (fitted with a small heavy bob that is connected with a metal rod) is $5\, seconds$ fast each day at a temperature of $15\,^oC$ and $10\,seconds$ slow at a temperature of $30\,^oC$. The temperature at which it is designed to give correct time, is …….. $^oC$

A cylindrical metal rod of length $L‌‌_0$ is shaped into a ring with a small gap as shown. On heating the system

The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and  $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of vessel  $A$  is $\alpha$, the coefficient of linear expansion of vessel $B$ is

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of $57\,^oC$ is drunk. You can take body (tooth) temperature to be $37\,^oC$ and $\alpha = 1.7 \times  10^{-5}/^oC$, bulk modulus for copper $ = 140 \times 10^9\, N/m^2 $.

An iron bar of length $10\, m$ is heated from $0°C$ to $100°C.$ If the coefficient of linear thermal expansion of iron is $ 10 \times 10^{-6}{°C^{-1}}$, the increase in the length of bar is  ………. $cm$