Mechanical Properties of Solids Test

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Mechanical Properties of Solids Test - 52

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Weekly Quiz Competition

Question 1
1 / -0

The dimensions of four wires of the same material are given below. In which wire the increase in the length will be maximum?

A
Length 100 cm, diameter 1 mm

B
Length 200 cm, diameter 2 mm

C
Length 300 cm. diameter 3 mm

D
Length 50 cm, diameter 0.5 mm

Solution

Sln :
$$Y \, = \, \dfrac{Fla}{\Delta lll} \, = \, \dfrac{Fl}{a \Delta l} \, or \, \Delta l \, \, or \, \dfrac{1}{D^2}$$

a. $$\dfrac{100}{l^2} \, = \, 100$$

b. $$\dfrac{200}{4} \, = \, 50$$

c. $$\dfrac{300}{9} \, = \, 33.33$$

d. $$\dfrac{50}{(1/2)^2} \, = \, 200$$
Question 2
1 / -0

A steel wire 2 m long is suspended from the ceiling. When a mass is hung at its lower end, the increase in length recorded is 1 cm. Determine the strain in the wire.

A
$$5 \, \times 10^{-3}$$

B
$$65 \, \times 10^{-3}$$

C
$$6 \, \times 10^{-3}$$

D
$$7 \, \times 10^{-3}$$

Solution

Strain$$=\cfrac { \triangle L }{ L } =\cfrac { 0.01m }{ 2m } $$
$$=0.01\times 0.5$$
$$=0.005$$
$$=5\times { 10 }^{ -3 }$$
Question 3
1 / -0

The edges of an aluminmum cube are $$10\ cm$$ 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. Shear modulus of aluminium is $$25\times 10^{9} Pa$$, the vertical deflection in the face to which mass is attached is

A
$$4\times 10^{-4} m$$

B
$$4 \times 10^{-7} m$$

C
$$25 \times 10^{-6} m$$

D
$$6 \times 10^{-7} m$$

Solution

The situation as is shown in the figure. A force of 100g acts on farther face of cube as shown, due to which shear will develop.
$$\eta \,= \,\dfrac{F/A}{x/l}$$
$$x \,= \,\dfrac{Fl}{A \eta} \,= \,\dfrac{100 \times l }{l^2 \times 25 \times 10^9}$$
$$x \,= \,4 \times 10^{-7} m$$
Question 4
1 / -0

A wire is stretched 1 mm by a force of 1 kN. How far would a wire of the same material and length but of four times that diameter he stretched by the same force?

A
$$\dfrac{1}{2}$$mm

B
$$\dfrac{1}{4}$$mm

C
$$\dfrac{1}{8}$$mm

D
$$\dfrac{1}{16}$$mm

Solution

$$Y \, = \, \dfrac{Fl}{a\Delta l}$$
Y, l and F are constants.
$$\therefore \, \Delta l \, \, or \, \dfrac{1}{D^2}$$

$$\dfrac{\Delta l_2}{\Delta l_1} \, = \, \dfrac{d_1^2}{D_2^2} \, = \, \dfrac{1}{16}$$

$$\therefore \, \Delta l_2 \, = \, \dfrac{1}{16} \, mm$$
Question 5
1 / -0

A steel wire is stretched by 1 kg wt. If the radius of the wire is doubled, its Young's modulus will:

A
remain unchanged

B
become half

C
become double

D
become four times

Solution

Youngs modulus is the property of material; it does not depend on shape and size of body.
Question 6
1 / -0

Plastic deformation results from the following

A
Slip

B
Twinning

C
Both slip and twinning

D
creep

Solution

Two prominent mechanisms of plastic deformation, namely slip and twinning occur .
1. Slip involves sliding of blocks of crystal over one other along definite crystallographic planes, called slip planes. During slip each atom usually moves same integral number of atomic distances along the slip plane producing a step, but the orientation of the crystal remains the same.

2. Portion of crystal takes up an orientation that is related to the orientation of the rest of the untwined lattice in a definite, symmetrical way. The twinned portion of the crystal is a mirror image of the parent crystal.
Question 7
1 / -0

A rubber ball of bulk modulus B is taken to a depth h of a liquid of density p. Find the fractional change in the radius of the ball.

A

$$ \, \dfrac{\rho gh}{4B}$$

B

$$ \, \dfrac{\rho gh}{3B}$$

C

$$\, \dfrac{\rho gh}{2B}$$

D

$$ \dfrac{\rho gh}{5B}$$

Solution

$$\dfrac{\delta V}{V} \, = \, -\dfrac{P}{B}$$
Where $$P \, = \, \rho gh$$
Then $$-\dfrac{\delta V}{V}\, = \, \dfrac{\rho gh}{B}$$
Since, the volume of the sphere is V = $$\dfrac{4}{3}\pi r^{3}$$, we have
$$\dfrac{\delta V}{V}\, = \, \dfrac{3\delta r}{r}$$
Using Eqs, (i) and (ii), we have

$$\dfrac{\delta r}{r}\, = \, \dfrac{\rho gh}{3B}$$
Question 8
1 / -0

A thin metal sheet is being bent by or pounded in to a new shape. The process of being elastic to plastic behaviour is known as

A
Yield

B
Creep

C
Welding

D
Tinkering

Solution

The yield point is the point on a stressstrain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Yielding means the start of breaking of fibers.

The correct option is option(a)
Question 9
1 / -0

An elastic spring is given a force of 1000 N over an area of $$0.2 m^2.$$

A
$$3000 N m^{-2}$$

B
$$5000 N m^{-2}$$

C
$$500 N m^{-2}$$

D
$$2500 N m^{-2}$$

Solution

Stress is defined by Stress = $$1000/0.2=5000 Nm^{-2}$$

The correct option is option (b)
Question 10
1 / -0

The plasticity behaviour of a material determines the

A
elastic behavior of the material

B
resistance of the material to electric fields

C
viscous behavior of the material and is irrecoverable.

D
resistance of the material to magnetic fields

Solution

Plasticity is defined as the property which enables a material to be deformed continuously and permanently without rupture during the application of force. This deformation determines the viscous behavior of the material and is irrecoverable.

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Mechanical Properties of Solids Test - 52

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Mechanical Properties of Solids Test - 52

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SHARING IS CARING

Question 1

Length 100 cm, diameter 1 mm

Length 200 cm, diameter 2 mm

Length 300 cm. diameter 3 mm

Length 50 cm, diameter 0.5 mm

Solution

Question 2

$$5 \, \times 10^{-3}$$

$$65 \, \times 10^{-3}$$

$$6 \, \times 10^{-3}$$

$$7 \, \times 10^{-3}$$

Solution

Question 3

$$4\times 10^{-4} m$$

$$4 \times 10^{-7} m$$

$$25 \times 10^{-6} m$$

$$6 \times 10^{-7} m$$

Solution

Question 4

$$\dfrac{1}{2}$$mm

$$\dfrac{1}{4}$$mm

$$\dfrac{1}{8}$$mm

$$\dfrac{1}{16}$$mm

Solution

Question 5

remain unchanged

become half

become double

become four times

Solution

Question 6

Slip

Twinning

Both slip and twinning

creep

Solution

Question 7

$$ \, \dfrac{\rho gh}{4B}$$

$$ \, \dfrac{\rho gh}{3B}$$

$$\, \dfrac{\rho gh}{2B}$$

$$ \dfrac{\rho gh}{5B}$$

Solution

Question 8

Yield

Creep

Welding

Tinkering

Solution

Question 9

$$3000 N m^{-2}$$

$$5000 N m^{-2}$$

$$500 N m^{-2}$$

$$2500 N m^{-2}$$

Solution

Question 10

elastic behavior of the material

resistance of the material to electric fields

viscous behavior of the material and is irrecoverable.

resistance of the material to magnetic fields

Solution

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