A rod of length $20\, cm$ is made of metal. It expands by $0.075cm$ when its temperature is raised from $0°C$ to $100°C.$ 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 $B$. This rod expands by $0.060\, cm$ for the same change in temperature. The portion made of metal $A$ has the length ........ $cm$
$20$
$10$
$15$
$18$
A steel rod with ${y}=2.0 \times 10^{11} \,{Nm}^{-2}$ and $\alpha=10^{-5}{ }^{\circ} {C}^{-1}$ of length $4\, {m}$ and area of cross-section $10\, {cm}^{2}$ is heated from $0^{\circ} {C}$ to $400^{\circ} {C}$ without being allowed to extend. The tension produced in the rod is ${x} \times 10^{5} \, {N}$ where the value of ${x}$ is ....... .
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 $K _1 / K _2=$ . . . . .
On heating a liquid of coefficient of cubical expansion $ \gamma$ in a container having coefficient of linear expansion $ \gamma / 3$, the level of liquid in the container will
A solid ball of metal has a concentric spherical cavity within it. If the ball is heated, the volume of the cavity will
The coefficient of volumetric expansion of mercury is $18 × 10^{-5}{°C^{-1}}$. A thermometer bulb has a volume $10^{-6}\, m^3$ and cross section of stem is $ 0.004 \,cm^2$. Assuming that bulb is filled with mercury at $0°C$ then the length of the mercury column at $100°C$ is