Q. A metallic container is completely filled with liquid. The coefficient of linear expansion of the metal is $2.0 \times 10^{-6}$ per $^{\circ} C$ and the coefficient of cubical expansion of the liquid is $6.0 \times 10^{-6}$ per ${ }^{\circ} C$. On heating the vessel :

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A

The liquid will overflow

B

The level of the liquid will fall

C

The level of the liquid will remain unchanged

D

The level of liquid will rise or fall depending on the nature of the metal and of the liquid

Solution:

Coefficient of cubical expansion of container,
$\gamma_{c} =3 \alpha_{c}=3 \times 2 \times 10^{-6}\, {}^{\circ}C ^{-1}$
$=6 \times 10^{-6}\,{}^ {\circ} C ^{-1}$
Coefficient of cubical expansion of liquid,
$\gamma_{l}=6 \times 10^{-6}\, {}^{\circ}C ^{-1}$
Thus, both container and liquid will expand to same extent and level of liquid remain unchanged.

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Q. A metallic container is completely filled with liquid. The coefficient of linear expansion of the metal is $2.0 \times 10^{-6}$ per $^{\circ} C$ and the coefficient of cubical expansion of the liquid is $6.0 \times 10^{-6}$ per ${ }^{\circ} C$. On heating the vessel :

The liquid will overflow

The level of the liquid will fall

The level of the liquid will remain unchanged

The level of liquid will rise or fall depending on the nature of the metal and of the liquid

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1. If the temperature difference on the two sides of a wall increases from $ 100{}^\circ C $ to $ 200{}^\circ C $ , its thermal conductivity

2. A wall is made of equally thick layers $A$ and $B$ of different materials. Thermal conductivity of $A$ is twice that of $B$. In the steady state, the temperature difference across the wall is $36^{\circ}C$. The temperature difference across the layer $A$ is

3. The radiation emitted by a star $A$ is $10,000$ times that of the sun. If the surface temperatures of the sun and the star $A$ are $8000 \, K$ and $2000 \, K$ respectively. The ratio of the radii of the star $A$ and the sun is

4. A black body at $1373$ $℃$ emits maximum energy corresponding to a wavelength of $1.78$ microns. The temperature of the moon for which $\lambda _{m}=14$ micron would be

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1. If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

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3. A car starts from rest and accelerates at $5\, m / s ^{2}$ At $t=4\, s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t =6\, s$ ? (Take $\left. g =10\, m / s ^{2}\right)$

4. A wheel with $20$ metallic spokes each $1\, m$ long is rotated with a speed of $120\, rpm$ in a plane perpendicular to a magnetic field of $0.4\, G$. The induced emf between the axle and rim of the wheel will be, $(1 G = 10^{-4}\, T)$

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