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 the vessel $A$ is $\alpha $, then coefficient of linear expansion of $B$
$\frac{{\alpha {\gamma _1}{\gamma _2}}}{{{\gamma _1} + {\gamma _2}}}$
$\frac{{{\gamma _1} - {\gamma _2}}}{{2\alpha }}$
$\frac{{{\gamma _1} - {\gamma _2} + \alpha }}{3}$
$\frac{{{\gamma _1} - {\gamma _2}}}{3} + \alpha $
A pendulum clock keeps correct time at $0\ ^oC$. The thermal coefficient of linear expansion of the material of the pendulum is $\alpha$. If the temperature rises to $t\ ^oC$, then the clock loses per day by (in second)
A rod of length $20 \,\,cm$ is made of metal. It expands by $0.075\,\, cm$ when its temperature is raised from $0^o C$ to $100^o C$. Another rod of a different metal $B$ having the same length expands by $0.045 cm$ for the same change in temperature, a third rod of the same length is composed of two parts one of metal $A$ and the other of metal $B$. Thus rod expand by $0.06 \,\,cm$.for the same change in temperature. The portion made of metal $A$ has the length .............. $cm$
If an electric heater is rated at $1000\,W$, then the time required to heat one litre of water from $20\,^oC$ to $60\,^oC$ is
Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is held at a temperature of $100^{\circ} C$, while the other one is kept at $0^{\circ} C$. If the two are brought into contact, then assuming no heat loss to the environment, the final temperature that they will reach is
Two large holes are cut in a metal sheet. If this is heated, distances $AB$ and $BC$, (as shown)