## H C VERMA PHYSICS BOOK SOLUTIONS MECHANICAL PROPERTIES OF MATTER

# Solved Examples

3. A steel wire of length 2.0 m is stretched through 2.0 mm. The cross-sectional area of the wire is 4.0 mm^{2}. Calculate the elastic potential energy stored in the wire

in the stretched condition. Young’s modulus of steel = 2.0 × 1011 N/m^{2}.

4. Water is kept in a beaker of radius 5.0 cm. Consider a diameter of the beaker on the surface of the water. Find the force by which the surface on one side of the

diameter pulls the surface on the other side. Surface tension of water = 0.075 N/m.

5. A water drop of radius 10^{–2} m is broken into 1000 equal droplets. Calculate the gain in surface energy. Surface tension of water is 0.075 N/m.

Sol. The volume of the original drop is

6. Find the excess pressure inside a mercury drop of radius 2.0 mm. The surface tension of mercury = 0.464 N/m.

Sol. The excess pressure inside the drop is

P_{2} = P_{1} = 2S/R

7. A 0.02 cm liquid column balances the excess pressure inside a soap bubble of radius 7.5 mm. Determine the density of the liquid. Surface tension of soap solution = 0.03 N/m.

Sol. The excess pressure inside a soap bubble is

8. A capillary tube of radius 0.20 mm is dipped vertically in water. Find the height of the water column raised in the tube. Surface tension of water = 0.075 N/m and density of water = 1000 kg/m^{3}. Take g = 10 m/s^{2}.

Sol. We have,

9. An air bubble of diameter 2 mm rises steadily through a solution of density 1750 kg/m^{3} at the rate of 0.35 cm/s. Calculate the coefficient of viscosity of the solution. The density of air is negligible.

Sol.The force of buoyancy B is equal to the weight of the displaced liquid. Thus,

## Questions for Short answer

1. The ratio stress/strain remains constant for small deformation of

3. When the skeleton of an elephant and the skeleton of a mouse are prepared in the same size, the bones of the elephant are shown thicker than those of the mouse.

Explain why the bones of an elephant are thicker than proportionate. The bones are expected to withstand the stress due to the weight of the animal.

4. The yield point of a typical solid is about 1%. Suppose you are lying horizontally and two persons are pulling your hands and two person are pulling your legs

along your own length. How much will be the increase in your length if the strain is 1%? Do you think your yield point is 1% or, much less than that ?

5. When rubber sheets are used in a shock absorber, what happens to the energy of vibration?

6. If a compressed spring is dissolved in acid, what happens to the elastic potential energy of the spring ?

7. A steel blade placed gently on the surface of water floats on it. If the same blade is kept will inside the