NCERT Class 11 Part 2 - Physics

Anup Kumar Rajput, Shweta Uppal, Arun Chitkara

Chapter 9

Mechanical Properties Of Solids - all with Video Answers

Educators

Chapter Questions

Problem 1

A steel wire of length $4.7 \mathrm{~m}$ and cross-sectional area $3.0 \times 10^{-5} \mathrm{~m}^{2}$ stretches by the same amount as a copper wire of length $3.5 \mathrm{~m}$ and cross-sectional area of $4.0 \times 10^{-5} \mathrm{~m}^{2}$ under a given load. What is the ratio of the Young's modulus of steel to that of copper?

Ajay Singhal

Ajay Singhal

Numerade Educator

Problem 2

Figure $9.11$ shows the strain-stress curve for a given material. What are (a) Young's modulus and (b) approximate yield strength for this material?

Ajay Singhal

Numerade Educator

Problem 3

Fig. $9.11$ The stress-strain graphs for materials $A$ and $B$ are shown in Fig. $9.12$.
The graphs are drawn to the same scale.
(a) Which of the materials has the greater Young's modulus?
(b) Which of the two is the stronger material?

Ajay Singhal

Numerade Educator

Problem 4

Read the following two statements below carefully and state, with reasons, if it is true or false.
(a) The Young's modulus of rubber is greater than that of steel:
(b) The stretching of a coil is determined by its shear modulus.

Ajay Singhal

Numerade Educator

Problem 5

Two wires of diameter $0.25 \mathrm{~cm}$, one made of steel and the other made of brass are loaded as shown in Fig. 9.13. The unloaded length of steel wire is $1.5 \mathrm{~m}$ and that of brass wire is $1.0 \mathrm{~m}$. Compute the elongations of the steel and the brass wires.

Ajay Singhal

Numerade Educator

Problem 6

The edge of an aluminium cube is $10 \mathrm{~cm}$ long. One face of the cube is firmly fixed to a vertical wall. A mass of $100 \mathrm{~kg}$ is then attached to the opposite face of the cube. The shear modulus of aluminium is $25 \mathrm{GPa}$. What is the vertical deflection of this face?

Ajay Singhal

Numerade Educator

Problem 7

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50,000 \mathrm{~kg}$. The inner and outer radii of each column are 30 and $60 \mathrm{~cm}$ respectively. Assuming the load distribution to be uniform. calculate the compressional strain of each column.

Ajay Singhal

Numerade Educator

Problem 8

A piece of copper having a rectangular cross-section of $15.2 \mathrm{~mm} \times 19.1 \mathrm{~mm}$ is pulled in tension with $44,500 \mathrm{~N}$ force, producing only elastic deformation. Calculate the resulting strain?

Ajay Singhal

Numerade Educator

Problem 9

A steel cable with a radius of $1.5 \mathrm{~cm}$ supports a chairlift at a ski area. If the maximum stress is not to exceed $10^{8} \mathrm{~N} \mathrm{~m}^{-2}$, what is the maximum load the cable can support?

Ajay Singhal

Numerade Educator

Problem 10

A rigid bar of mass $15 \mathrm{~kg}$ is supported symmetrically by three wires each $2.0 \mathrm{~m}$ long. Those at each end are of copper and the middle one is of iron. Determine the ratios of their diameters if each is to have the same tension.

Ajay Singhal

Numerade Educator

Problem 11

A $14.5 \mathrm{~kg}$ mass, fastened to the end of a steel wire of unstretched length $1.0 \mathrm{~m}$, is whirled in a vertical circle with an angular velocity of $2 \mathrm{rev} / \mathrm{s}$ at the bottom of the circle. The cross-sectional area of the wire is $0.065 \mathrm{~cm}^{2} .$ Calculate the elongation of the wire when the mass is at the lowest point of its path.

Ajay Singhal

Numerade Educator

Problem 12

Compute the bulk modulus of water from the following data: Initial volume $=100.0$ litre, Pressure increase $=100.0 \mathrm{~atm}\left(1 \mathrm{~atm}=1.013 \times 10^{5} \mathrm{~Pa}\right)$, Final volume $=100.5$ litre. Compare the bulk modulus of water with that of air (at constant temperature). Explain in simple terms why the ratio is so large.

Ajay Singhal

Numerade Educator

Problem 13

What is the density of water at a depth where pressure is $80.0 \mathrm{~atm}$, given that its density at the surface is $1.03 \times 103 \mathrm{~kg} \mathrm{~m}^{-3} ?$

Hast Aggarwal

Numerade Educator

Problem 14

Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of $10 \mathrm{~atm}$.

Ajay Singhal

Numerade Educator

Problem 15

Determine the volume contraction of a solid copper cube, $10 \mathrm{~cm}$ on an edge, when subjected to a hydraulic pressure of $7.0 \times 10^{6} \mathrm{~Pa}$.

Ajay Singhal

Numerade Educator

Problem 16

How much should the pressure on a litre of water be changed to compress it by $0.10 \%$ ?

Ajay Singhal

Numerade Educator

Problem 17

Anvils made of single crystals of diamond, with the shape as shown in Fig. 9.14, are used to investigate behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of $0.50 \mathrm{~mm}$, and the wide ends are subjected to a compressional force of $50,000 \mathrm{~N}$. What is the pressure at the tip of the anvil?

Ajay Singhal

Numerade Educator

Problem 18

A rod of length $1.05 \mathrm{~m}$ having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown in Fig. 9.15. The cross-sectional areas of wires $\mathrm{A}$ and $\mathrm{B}$ are $1.0 \mathrm{~mm}^{2}$ and $2.0 \mathrm{~mm}^{2}$. respectively. At what point along the rod should a mass $m$ be suspended in order to oroduce (a) equal stresses and (b) equal strains in both steel and aluminium wires.

Mayukh Banik

Numerade Educator

Problem 19

A mild steel wire of length $1.0 \mathrm{~m}$ and cross-sectional area $0.50 \times 10^{-2} \mathrm{~cm}^{2}$ is stretched, well within its elastic limit, horizontally between two pillars. A mass of 100 $\mathrm{g}$ is suspended from the mid-point of the wire. Calculate the depression at the midpoint.

Narayan Hari

Numerade Educator

Problem 20

Two strips of metal are riveted together at their ends by four rivets, each of diameter $6.0$
$\mathrm{mm}$. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed $6.9 \times 10^{7} \mathrm{~Pa}$ ? Assume that each rivet is to carry one quarter of the load.

Ajay Singhal

Numerade Educator

Problem 21

The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven $\mathrm{km}$ beneath the surface of water. The water pressure at the bottom of the trench is about $1.1 \times 10^{8} \mathrm{~Pa}$. A steel ball of initial volume $0.32 \mathrm{~m}^{3}$ is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom?

Ajay Singhal

Numerade Educator