A bakelite beaker has volume capacity of $500\, cc$ at $30^{\circ} C$. When it is partially filled with $V _{ m }$ volume (at $30^{\circ}$ ) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If $\gamma_{\text {(beaker) }}=6 \times 10^{-6}{ }^{\circ} C ^{-1}$ and $\gamma_{(\text {mercury })}=1.5 \times 10^{-4}{ }^{\circ} C ^{-1},$ where $\gamma$ is the coefficient of volume expansion, then $V _{ m }($in $cc )$ is close to

A bar of iron is $10\, cm$ at $20°C$. At $19°C$ it will be ($\alpha$ of iron $= 11 \times 10^{-6}/°C$)

Draw graph of $\alpha _V$ temperature.

A uniform cylindrical rod of length $L$ and radius $r$, is made from a material whose Young's modulus of Elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to

A steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^oC$ so that it cannot contract on cooling. The tension in the rod at $0\,^oC$ is approximately ……… $N$ $(\alpha = 10^{-5}/\,^oC,\,\,Y = 2 \times 10^{11}\,N/m^2)$