H C Verma Solutions for Chapter: Some Mechanical Properties of Matter, Exercise 4: EXERCISES

A capillary tube of radius $1 \mathrm{mm}$ is kept vertical with the lower end in water.

(a) Find the height of water raised in the capillary.

(b) If the length of the capillary tube is half the answer of part (a), find the angle made by the water surface in the capillary with the wall.

The lower end of a capillary tube of radius $1 \mathrm{mm}$ is dipped vertically into mercury.

(a) Find the depression of mercury column in the capillary.
(b) If the length dipped inside is half the answer of part (a), find the angle made by the mercury surface at the end of the capillary with the vertical.

The surface tension of mercury is $0.465 \mathrm{N} {\mathrm{m}}^{-1}$ and the contact angle of mercury with the glass $135°$.

Two large glass plates are placed vertically and parallel to each other inside a tank of water with a separation between the plates equal to $1 \mathrm{mm}$. Find the rise of water in the space between the plates. The surface tension of water is $0.075 \mathrm{N} {\mathrm{m}}^{-1}$.

Consider an ice cube of edge $1.0 \mathrm{cm}$, kept in a gravity-free hall. The surface area of the water when the ice melts is given by $(36\mathrm{\pi }{)}^{\frac{1}{n}} {\mathrm{cm}}^2$. Then find the value of $n$. Neglect the difference in densities of ice and water.

A wire forming a loop is dipped into the soap solution and taken out so that a film of soap solution is formed. A loop of $6.28 \mathrm{cm}$ long thread is gently put on the film, and the film is pricked with a needle inside the loop. The thread loop takes the shape of a circle. The surface tension of the soap solution is $0.030 \mathrm{N} {\mathrm{m}}^{-1}$. The tension In the thread is given by $k\times {10}^{-4} \mathrm{N}$. Find the value of $k$.

A metal sphere of radius $1 \mathrm{mm}$ and mass $50 \mathrm{mg}$ falls vertically in glycerine.

(a) The viscous force exerted by the glycerine on the sphere when the speed of the sphere is $1 \mathrm{cm} {\mathrm{s}}^{-1}$ is $x$.

(b) The hydrostatic force exerted by the glycerine on the sphere is $y$. 

(c) The terminal velocity with which the sphere will move down without acceleration is $z$

The density of glycerine is $1260 \mathrm{kg} {\mathrm{m}}^{-3}$ and its coefficient of viscosity at room temperature is $8.0 \mathrm{poise}$. Find the value of $\frac{x}{y}z$ in $cm s^{-1}$.

Estimate the speed of the vertically falling raindrops from the following data. The radius of drops is $0.02 \mathrm{cm}$, the viscosity of air is $1.8\times {10}^{-4} \text{poise}$, $g=9.9\times 10 \mathrm{m} {\mathrm{s}}^{-2}$ and the density of water is$1000 \mathrm{kg} {\mathrm{m}}^{-3}$. (Speed $\mathrm{m} {\mathrm{s}}^{-1}$)

Water flows at a speed of $6 \mathrm{cm} {\mathrm{s}}^{-1}$ through a tube of radius $1 \mathrm{cm}$. The coefficient of the viscosity of water at room temperature is $0.01 \text{poise}$. Calculate the Reynolds number. Is it a steady flow?