Mechanical Properties of Solids Test

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Mechanical Properties of Solids Test - 31

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Question 1
1 / -0

A spiral spring is stretched by a weight attached to it. The strain is

A
shear

B
elastic

C
tensile

D
bulk

Solution

It's normal to the cross-section and causes bending which induces tensile as well as compressive stresses in it. Thus the correct answer is C.
Question 2
1 / -0

A $$10 \ meter$$ long thick rubber pipe is suspended from one of its ends. The extension produced in the pipe under its own weight will be :$$(Y=5\times10^{6}N/m^{2}$$ and density of rubber =$$ 1500 \ kg/m^{3}$$)

A
$$1.5\ m$$

B
$$0.15\ m$$

C
$$0.015 \ m$$

D
$$0.0015 \ m$$

Solution

$$\Delta l=\dfrac { FL }{ AY } =\dfrac { \dfrac { mg }{ 2 } L }{ AY } \quad (average\quad force\quad due\quad to\quad weight\quad at\quad centre\quad of\quad mass=\dfrac { mg }{ 2 } )\\ \\ =\dfrac { (1500\times A\times L\times g).L }{ 2AY } =\dfrac { 1500\times 10\times 10\times 10 }{ 2\times 5\times 1{ 0 }^{ 6 } } =0.15m$$
Question 3
1 / -0

A petite young woman of $$50\ kg$$ distributes her weight equally over her high-heeled shoes. Each heel has an area of $$0.75cm^2$$. Find the pressure exerted by each heel? Take $$g=10 m/s^2$$

A
$$6.66\times10^{6}Pa$$

B
$$3.33\times10^{6}Pa$$

C
$$1.67\times10^{6}Pa$$

D
$$4.44\times10^{6}Pa$$

Solution

Pressure on each heel is :
$$P=\dfrac {W/2}{A}$$
$$P=\dfrac {25\times 10}{0.75\times 10^{-4}}=3.33\times 10^6\ Pa$$
Question 4
1 / -0

Proof resilience is related to

A
PE stored in an elastic body

B
stiffness of a beam

C
elastic fatigue

D
elastic relaxation

Solution

Proof resilience is defined as the maximum energy that can be absorbed within the elastic limit, without creating a permanent distortion.
Option A.
Question 5
1 / -0

Outside a house, $$1 km$$ from ground zero of a $$100 $$ kiloton nuclear bomb explosion, the pressure will rapidly rise to as high as $$2.8$$ atm while the pressure inside the house is $$1$$ atm. If the area outside the house is $$50\:m^2$$. The resulting net force exerted by the air in front of the house is :

A
$$9.1\times10^{6}N$$

B
$$2.1\times10^{7}N$$

C
$$1.41\times10^{7}N$$

D
$$1.63\times10^{7}N$$

Solution

Pressure difference at the boundary of house$$= 2.8$$ atm-$$1$$ atm$$ =1.8$$ atm
So force exerted $$=PA=$$($$1.8$$ atm)($$50$$) $$=1.8\times 101325 \times50 = 9.1\times 10^6N$$
Question 6
1 / -0

A wire $$1 m$$ long has cross-section $$1 mm^{2}$$ and $$Y = 1.2\times10^{11}Pa$$. Find the work done in stretching it by $$2 mm.$$

A
2.4J

B
0.24J

C
0.024J

D
1.2J

Solution

Work done in stretching is the potential energy stored which is given as
$$U=\dfrac{1}{2}VY\epsilon^2=\dfrac{1}{2}(1\times 10^{-6})\times (1.2\times 10^{11})\times(\dfrac{2\times 10^{-3}}{1})^2=0.24 J$$
Question 7
1 / -0

If S is the stress and Y is Young's modulus of the material of a wire, the energy stored in the wire per unit volume is :

A
$$2S^{2}Y$$

B
$$\displaystyle \frac{S^{2}}{2Y}$$

C
$$\displaystyle \frac{2Y}{S^{2}}$$

D
$$\displaystyle \frac{S}{2Y}$$

Solution

Energy stored per unit volume can be given as:
$$E =\dfrac{1}{2} \times stress \times strain $$ -----------(1)
From Hooke's law :
Young's modulus, $$Y = \dfrac{Stress}{Strain}$$

$$\implies$$ $$Strain = \dfrac{Stress}{Y} = \dfrac{S}{Y}$$ -----------(2)

From equation (1) and (2):
$$\therefore$$ $$E = \dfrac{1}{2} \times S \times \dfrac{S}{Y} $$

$$\Rightarrow E= \dfrac{1}{2} \dfrac{S^2}{Y}$$
Hence, the correct option is $$(B)$$
Question 8
1 / -0

A gas undergoes a process in which its pressure P and volume V are related as $$VP^n=$$ constant. The bulk modulus for the gas in this process is:

A
np

B
p$$^{1/n}$$

C
$$\dfrac{p}{n}$$

D
p$$^n$$

Solution

$$Vp^n=$$constant
$$B=\dfrac{\Delta p}{(\dfrac{\Delta V}{V})}$$ where B is Bulk modulus
Differentiate on both sides w.r.t,
$$p^n+np^{n-1}\dfrac{\Delta p .V}{\Delta V}=0$$
$$p^{n-1}(p+\dfrac{n\Delta p}{\Delta V}.V)=0$$
$$p=0$$
$$p+n\dfrac{\Delta p}{\Delta V/V}=0$$
$$p-nB=0$$
$$B=\dfrac{p}{n}$$
Question 9
1 / -0

A vertical steel post of diameter $$25 cm$$ and length $$2.5 m$$ supports a weight of $$8000 kg$$. Find the change in length produced.
(Given $$Y=2\times 10^{11}Pa$$)

A
2.1 cm

B
0.21 cm

C
0.21 mm

D
0.021 mm

Solution

$$\displaystyle \Delta l=\frac{Fl}{AY}=\frac{4\times8000\times10\times2.5}{\pi (.25)^{2}\times2\times10^{11}}=\frac{4\times16\times10^{-6}}{\pi}=0.021mm$$
Question 10
1 / -0

Which one of the following substance possesses the highest elasticity?

A
rubber

B
glass

C
steel

D
copper

Solution

Modulus of elasticity gives the idea of elasticity. For above materials, values of E are:
Glass: $$50-90 GPa$$
Rubber:$$ 0.01-0.1 GPa$$
Steel:$$ 200 GPa$$
Copper: $$117 GPa$$

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Mechanical Properties of Solids Test - 31

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Mechanical Properties of Solids Test - 31

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SHARING IS CARING

Question 1

shear

elastic

tensile

bulk

Solution

Question 2

$$1.5\ m$$

$$0.15\ m$$

$$0.015 \ m$$

$$0.0015 \ m$$

Solution

Question 3

$$6.66\times10^{6}Pa$$

$$3.33\times10^{6}Pa$$

$$1.67\times10^{6}Pa$$

$$4.44\times10^{6}Pa$$

Solution

Question 4

PE stored in an elastic body

stiffness of a beam

elastic fatigue

elastic relaxation

Solution

Question 5

$$9.1\times10^{6}N$$

$$2.1\times10^{7}N$$

$$1.41\times10^{7}N$$

$$1.63\times10^{7}N$$

Solution

Question 6

2.4J

0.24J

0.024J

1.2J

Solution

Question 7

$$2S^{2}Y$$

$$\displaystyle \frac{S^{2}}{2Y}$$

$$\displaystyle \frac{2Y}{S^{2}}$$

$$\displaystyle \frac{S}{2Y}$$

Solution

Question 8

np

p$$^{1/n}$$

$$\dfrac{p}{n}$$

p$$^n$$

Solution

Question 9

2.1 cm

0.21 cm

0.21 mm

0.021 mm

Solution

Question 10

rubber

glass

steel

copper

Solution

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