Mechanical Properties of Solids Test

Result

Mechanical Properties of Solids Test - 81

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Weekly Quiz Competition

Question 1
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The radii and young's modulus of two uniform wires A & B are in the ratio 2:1 and 1:2 respectively. Both the wires are subjected to the same longitudinal force. If increase in the length of wire A is 1%. Then the percentage increase in length of wire B is

A
1

B
1.5

C
2

D
3

Solution
Question 2
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The apparatus used to determine Young's modulus of the material of a given wire is called

A
Newton's apparatus.

B
Wheatstone's apparatus

C
Searle's apparatus

D
Young's apparatus

Solution

$$ \begin{array}{l} \text { The apparatus used to determine Young's modulus of } \\ \text { the material of a given wire is called searle's. } \\ \text { apparatus. } \end{array} $$
Question 3
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The Young's experiment is performed with the lights of blue $$\left( \lambda =4360\mathring { A } \right) $$ and green colour $$\left( \lambda =5460\mathring { A } \right) ,$$ if the distance of the $${ 4 }^{ th }$$ fringe from the centre is x, then

A
$$x(Blue)=x(Green)$$

B
$$x(Blue)>x(Green)$$

C
$$x(green)<X(blue)$$

D
$$\dfrac { x(Blue) }{ x(Green) } =\dfrac { 5460 }{ 4360 } $$

Solution

Distance of $$n$$ bright fringe $$y_n =\dfrac {n\lambda D}{d}$$ i.e, $$y_n \propto \lambda$$

$$\therefore \dfrac {x_{n_1}}{x_{n_2}}=\dfrac {\lambda_1}{\lambda_2}\Rightarrow \dfrac {x(Blue)}{x(Green)}=\dfrac {4360}{5460}$$

$$\therefore x(Green) > x(Blue)$$
Question 4
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Two metal rods of the same length and area of crosssection are fixed ends to end between rigid supports. The materials of the rods have Young moduli $$\mathrm { Y } _ { 1 } \text { and } \mathrm { Y } _ { 2 }$$ , and coefficients of linear expansion $$\alpha _ { 1 } \text { and } \alpha _ { 2 }$$ and When rods are cooled the junction between the rods does not shift if:

A
$$Y _ { 1 } \alpha _ { 1 } = Y _ { 2 } \alpha _ { 2 }$$

B
$$Y _ { 1 } \alpha _ { 2 } = Y _ { 2 } \alpha _ { 1 }$$

C
$$Y _ { 1 } \alpha _ { 1 } ^ { 2 } = Y _ { 2 } \alpha _ { 2 } ^ { 2 }$$

D
$$Y _ { 1 } ^ { 2 } \alpha _ { 1 } = Y _ { 2 } ^ { 2 } \alpha _ { 2 }$$

Solution

$$ \begin{array}{l} Y_{1} \text { and } Y_{2} \text { are young modulus of rod } \\ \alpha_{1} \text { and } \alpha_{2} \text { are linear expansion coeffeient of rod } \\ \text { Giventhat, } \\ \text { There is no shift in Junction when vod were cooled } \end{array} $$
Which means.
Force exerted on both rod due to contraction will be equal
$$ \begin{aligned} \text { Force } &=\text { Stress } x \text { Area } \\ &=\text { young modulus } x \text { strain } x \text { Area } \end{aligned} $$
$$=Y_{x} \frac{\Delta L}{L} \times A$$
$$=Y_{x} \frac{K \alpha \Delta T}{K} \times A \quad \therefore \Delta L=L \alpha \Delta T$$ Force $$=Y_{x} \frac{\alpha \Delta T}{1} \times A$$
$$ \begin{array}{l} \text { (Force on rod) } \\ \qquad Y_{1} \alpha_{1} \Delta T A \quad=\quad(\text { Force on rod })_{2} \\ \Delta T \text { and } A \text { are same for both } \\ \qquad Y, \alpha_{1}=Y_{2} \alpha_{2} \end{array} $$
Question 5
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A metal wire is first stretched beyond its elastic limit and then released It

A
loses its elastic property completely and it will not contract.

B
will contract to its original length

C
will contract to its length at elastic limit

D
will contract but final length will be greater than original length

Solution
Question 6
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A copper wire and a steel wire of the same diameter and length 1m and 2m respectively are connected end to end and a force is applied which stretches their combined length by 1 cm. How much each wire is elongated respectively. Y of copper =1.2$$\times { 10 }^{ 4 }$$

A
0.45 cm, 0.55 cm

B
0.55 cm, 0.45 cm

C
0.45 cm, 0.55 cm

D
None

Solution
Question 7
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The Bulk modulus for an incompressible liquid is

A
Zero

B
Unity

C
Infinity

D
Between $$0$$ to $$1$$

Solution
Question 8
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The force constant of a wire does not depend on

A
Nature of the material

B
Radius of the wire

C
Length of the wire

D
none of these

Solution

$$K = \dfrac{YA}{L} =\dfrac{Y \times \pi r^2}{L} \implies K\ \propto\ \dfrac{Yr^2}{L}$$

i.e. force constant of a wire depends on Young's Modulus (nature of the material), radius of the wire and length of the wire.
Question 9
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A sound wave of wavelength $$0.31\,m$$ is travelling in air. The pressure at a point varied from $$(10^5 - 14)$$ pascal to $$(10^5 +14)$$ pascal and particles vibrate in $$SHM$$ with amplitude $$5.5\times 10^{-6}\,m.$$Bulk modulus of air is

A
$$1.2\times 10^5\,N/m^2$$

B
$$1.2 \times 10^3\,N/m^2$$

C
$$1.3 \times 10^4\,N/m^2$$

D
$$1.4 \times 10^5\,N/m^2$$

Solution
Question 10
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What will be the stress at $$-20^{o}C$$, if a steel rod with a cross-sectional area of $$150 mm^2$$ is stretched between two fixed points? The tensile load at $$20^{o}C$$ is $$5000 N $$ : ( Assume $$\alpha = 11.7 \times 10^{-6}/C$$ and $$Y = 200 \times 10^{11} N/m^2$$)

A
$$12.7 \times 10^{6} N/m^2$$

B
$$1.27 \times 10^{6} N/m^2$$

C
$$127 \times 10^{6} N/m^2$$

D
$$0.127 \times 10^{6} N/m^2$$