Angle of twist at free end
\(30^{0}=\frac{30}{180}\times \pi \ rad=\frac{\pi}{6} \ rad\)
Displacement of free surface
\(\Delta L=\frac{2\pi r}{2\pi}\times \frac{\pi}{6}\)
\(=\frac{\pi r}{6}=\frac{\pi \times 0.4}{6}cm\)
Angle of shear or shearing strain = \(\frac{\Delta L}{L}\)
\(=\frac{\pi \times 0.4}{6 \times 100}\ rad\)
\(=\frac{\pi \times 0.4}{6 \times 100} \times \frac{180}{\pi}\) degree = 0.12⁰

We know that h = \(\frac{2s cos\theta}{r \rho g}\)
Surface tension of hot water is less than the surface tension of cold water. Moreover, due to thermal expansion the radius of the capillary tube will increase in hot water. Due to both reasons, the height of capillary rise will be less in hot water as compared to cold water.

Steel is more elastic than rubber:
(i) We know that young's modulus is the ratio of stress to the strain. If the same force is applied to the wire of steel and rubber thread, which are of equal length and cross section area, we will find that the extension in the rubber thread is much greater than extension in steel wire.
(ii) Therefore, for a given stress, the strain produced in steel is much smaller than that produced in the rubber. This implies that young's modulus for steel is greater than that for rubber. Therefore, steel is more elastic than rubber.
Young's modulus of steel, \(Y_{s}=\frac{F}{A}=\frac{I}{\Delta I_{s}}\)
Young's modulus of rubber, \(Y_{r}=\frac{F}{A}=\frac{I}{\Delta I_{r}}\)
(iii) For same force applied to wires made of steel & rubber of same length and same area of cross section \(\Delta I_{s}<\Delta I_{r}\)
\(\frac{Y{s}}{Y_{r}}=\frac{\Delta I_{r}}{\Delta I_{s}}>1\)
ஃ Y_s>Y_r

(i) The oil used as a lubricant for heavy machinery parts should have a high viscous coefficient.
(ii) The highly viscous liquid is used to damp the motion of some instruments and is used as brake oil in hydraulic brakes.
(iii) Blood circulation through arteries and veins depends upon the viscosity of fluids.

(i) Atoms or molecules are tightly fixed.
(ii) Atoms get bound together through various types of bonding.
(iii) Due to the interaction between the atoms, they position themselves at a particular interatomic distance. Their mean positions.