A liquid with coefficient of volume expansion $\gamma$ is filled in a container of a material having the coefficient of linear expansion $\alpha$. If the liquid overflows on heating, then

- A
$\gamma = 3 \alpha$

- B
$\gamma > 3 \alpha$

- C
$\gamma < 3 \alpha$

- D
$\gamma > 3 \alpha^3$

The freezing point of the liquid decreases when pressure is increased, if the liquid

An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The diameter of tyre is $6\, mm$ smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of ........ $^oC$ (the coefficient of cubical expansion of iron is ${3.6 \times 10^{-5} } °C^{-1}$)

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

- [JEE MAIN 2021]

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T _1=300 K$ and $T _2=100 K$, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K _1$ and $K _2$ respectively. If the temperature at the junction of the two cylinders in the steady state is $200 K$, then $K _1 / K _2=$ . . . . .

- [IIT 2018]

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

- [IIT 2003]