A beaker is completely filled with water at $4°C$. It will overflow if

A metallic bar of Young's modulus, $0.5 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ and coefficient of linear thermal expansion $10^{-5}{ }^{\circ} \mathrm{C}^{-1}$, length $1 \mathrm{~m}$ and area of cross-section $10^{-3} \mathrm{~m}^2$ is heated from $0^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$ without expansion or bending. The compressive force developed in it is :

We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say $10\, cm$ We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that difference between their lengths remain constant. If  ${\alpha _{iron}}$ $= 1.2 \times 10^{-5}\,K^{-1}$ and ${\alpha _{brass}}$ $= 1.8 \times 10^{-5}\,K^{-1}$ what should we take as length of each strip ?

The coefficient of linear expansion depends on

Two different wires having lengths $L _{1}$ and $L _{2}$ and respective temperature coefficient of linear expansion $\alpha_{1}$ and $\alpha_{2},$ are joined end-to-end. Then the effective temperature coefficient of linear expansion is

The real coefficient of volume expansion of glycerine is $0.000597\, per°C$ and linear coefficient of expansion of glass is $0.000009\, per°C.$ Then the apparent volume coefficient of expansion of glycerine is