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**Exercise : ** Solutions of Questions on Page Number : **242**

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Q1 :
**
**

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

**Answer :**

Length of the steel wire, *L*_{1} = 4.7 m

Area of cross-section of the steel wire, *A*_{1} =
3.0 ×
10^{â€“5} m^{2}

Length of the copper wire, *L*_{2} = 3.5 m

Area of cross-section of the copper wire, *A*_{2} =
4.0 ×
10^{â€“5} m^{2}

Change in length = Δ*L*_{1}
= Δ*L*_{2} =
Δ*L*

Force applied in both the cases = *F*

Young's modulus of the steel wire:

… (*i*)

Young's modulus of the copper wire:

Dividing (*i*) by (*ii*), we get:

The ratio of Young's modulus of steel to that of copper is 1.79 : 1.

Answer needs Correction? Click Here

Q2 :
**
**

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?

**Answer :**

**(a)** It is clear from the given graph that for stress 150
× 10^{6} N/m^{2},
strain is 0.002.

∴Young's
modulus, *Y*

Hence, Young's
modulus for the given material is 7.5
×10^{10} N/m^{2}.

**(b)** The yield strength of a material is the maximum stress
that the material can sustain without crossing the elastic limit.

It is clear from the given graph that the approximate yield
strength of this material is 300 ×
10^{6} Nm/^{2} or 3
× 10^{8} N/m^{2}.

Answer needs Correction? Click Here

Q3 :
**
**

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?

**Answer :**

Q4 :
**
**

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.

**Answer :**

Q5 :
**
**

Two wires of diameter 0.25 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 m and that of brass wire is 1.0 m. Compute the elongations of the steel and the brass wires.

**Answer :**

Q6 :
**
**

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

**Answer :**

Q7 :
**
**

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

**Answer :**

Q8 :
**
**

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

**Answer :**

Q9 :
**
**

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

**Answer :**

Q10 :
**
**

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

**Answer :**

Q11 :
**
**

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

**Answer :**

Q12 :
**
**

Compute the bulk modulus of water from the following data:
Initial volume = 100.0 litre, Pressure increase = 100.0 atm (1
atm = 1.013 x 10^{5}
Pa), 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.

**Answer :**

Q13 :
**
**

What is the density of water at a depth where pressure is 80.0
atm, given that its density at the surface is 1.03
x 10^{3} kg
m^{-3}?

**Answer :**

Q14 :
**
**

Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.

**Answer :**

Q15 :
**
**

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

**Answer :**

Q16 :
**
**

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

**Answer :**

Q17 :
**
**

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 mm, and the wide ends are subjected to a compressional force of 50,000 N. What is the pressure at the tip of the anvil?

**Answer :**

Q18 :
**
**

A rod of length 1.05 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 **A** and **B** are 1.0
mm^{2} and 2.0 mm^{2}, respectively. At what
point along the rod should a mass *m* be suspended in order
to produce (a) equal stresses and (b) equal strains in both steel
and aluminium wires.

**Answer :**

Q19 :
**
**

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

**Answer :**

Q20 :
**
**

Two strips of metal are riveted together at their ends by four
rivets, each of diameter 6.0 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 x
10^{7} Pa? Assume that each rivet is to carry one quarter
of the load.

**Answer :**

Q21 :
**
**

The Marina trench is located in the Pacific Ocean, and at one
place it is nearly eleven km beneath the surface of water. The
water pressure at the bottom of the trench is about 1.1
x 10^{8} Pa. A steel
ball of initial volume 0.32 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?

**Answer :**

Physics Part-2 - Physics : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Mechanical Properties Of Solids ** will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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