Mechanical Properties of Solids Test

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Mechanical Properties of Solids Test - 35

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Weekly Quiz Competition

Question 1
1 / -0

A steel wire of length $$4.7\ m$$ and cross-sectional area $$3\times 10^{-6} m^{2}$$ stretches by the same amount as a copper wire of length $$3.5\ m$$ ad cross-sectional area of $$4\times 10^{-6} m^{2}$$ under a given load. The ratio of Young's modulus of steel to that of copper is

A
$$1.8$$

B
$$3.6$$

C
$$0.6$$

D
$$8.7$$

Solution

We know, $$\Delta l =\dfrac{FL}{AY}$$

Given, load and extension are same, thus, $$\dfrac{{Y}_{1}}{{Y}_{2}}=\dfrac{\dfrac{{L}_{1}}{{A}_{1}}}{\dfrac{{L}_{2}}{{A}_{2}}}=\dfrac{\dfrac{4.7}{3}}{\dfrac{3.5}{4}}=1.8$$
Question 2
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A iron bar of length $$l$$ cm and cross section $$A$$ $$cm^2$$ is pulled by a force of $$F$$ dynes iron ends so as to produce an elongation $$\Delta l$$ cm. Which of the following statement is correct?

A
Elongation is inversely proportional to length

B
Elongation is directly proportional to cross section $$A$$

C
Elongation is inversely proportional to $$A$$

D
Elongation is directly proportional to Young's module

Solution

$$\Delta l=\dfrac { FL }{ AY }$$
Thus, extension is inversely proportional to area. Only C statement is correct
Question 3
1 / -0

The longitudinal extension of any elastic material is very small. In order to have an appreciable change, the material must be in the form of

A
thin block of any cross section

B
thick block of any cross section

C
long thin wire

D
short thin wire

Solution

$$\Delta l =\dfrac{FL}{AY}$$
Thus, extension is directly proportional to length and inversely to area. Thus for appreciable extension, length must be long and area less, or long and thin wire
Question 4
1 / -0

A $$5\ kg$$ rod of square cross section $$5\ cm$$ on a side and $$1\ m$$ long is pulled along a smooth horizontal surface by a force applied at one end. The rod has a constant acceleration of $$2\ m/s^{2}$$. Determine the elongation in the rod. (Young's modulus of the material of the rod is $$5\times 10^{3} N/m^{9})$$.

A
Zero, as for elongation to be there, equal and opposite forces must act on the rod

B
Non-zero but cannot be determine from the given situation

C
$$4\mu m$$

D
$$16\mu m$$

Solution

Since it is pulled on a smooth surface from one end only, thus there wll be no elongation, as force will cause its displacement and not extension.
Question 5
1 / -0

A rubber rope of length $$8\ m$$ is hung from the ceiling of a room. What is the increase in length of rope due to its own weight? (Given : Young's modulus of elasticity of rubber $$= 5\times 106\ N/m$$ and density of rubber $$= 1.5\times 10^{3} kg/ m^{3}$$. Take $$g = 10\ m/s^{2})$$.

A
$$1.5mm$$

B
$$6mm$$

C
$$24mm$$

D
$$96mm$$

Solution

Weight of rubber $$W=mg=\rho ALg=$$$$8\times 1.5\times 10^3\times A\times g$$ , where $$A$$ is cross sectional area.
Elongation due to own weight is half of the elongation due to point load.
$$\Delta L=\dfrac{WL}{2AY}=\dfrac{8\times 1.5\times 10^3\times A\times L\times g}{2A\times 5\times 10^6 }=96\ mm$$
Question 6
1 / -0

The valve $$V$$ in the bent tube is initially kept closed. Two soap bubbles $$A$$ (smaller) and $$B$$ (larger) are formed at the two open ends of the tube. $$V$$ is now opened and air can flow freely between the bubbles.

A
There will be no change in the size of the bubbles

B
The bubbles will become of equal size

C
$$A$$ will become smaller and $$B$$ will become larger

D
The sizes of $$A$$ and $$B$$ will be interchanged

Solution

the soap bubbles form due to difference in outside and inside pressure so as the valve V is opened air molecules will move from right to left increasing inside pressure of small bubble and therefore it will further decrease in radius until it bursts. As the excess pressure is inversely proportional to radius of the bubble.
Question 7
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A metal rod of Young's modulus $$2\times 10^{10}Nm^{-2}$$ undergoes an elastic strain of $$0.06\%$$. The energy per unit volume stored in $$Jm^{-3}$$ is

A
$$3600$$

B
$$7200$$

C
$$10800$$

D
$$14400$$

Solution

Energy per unit volume$$ =\dfrac{1}{2}\times Stress \times Strain=\dfrac{1}{2} \times (Strain \times Y)\times Strain=\dfrac{1}{2} \times Y \times {(Strain)}^{2}$$
Thus, we get, $$0.5 \times 2\times {10}^{10} \times {(0.0006)}^{2}=3600$$
Question 8
1 / -0

Uniform rod of mass $$m$$, length $$l$$, area of cross-section $$A$$ has Young's modulus $$Y$$. If it is hanged vertically, elongation under its own weight will be :

A
$$\displaystyle\frac{mgl}{2AY}$$

B
$$\displaystyle\frac{2mgl}{AY}$$

C
$$\displaystyle\frac{mgl}{AY}$$

D
$$\displaystyle\frac{mgY}{Al}$$

Solution

$$Y=\displaystyle\frac{Fl}{A\Delta l}\Rightarrow \Delta l=\frac{Fl}{YA}=\frac{mgl}{YA}$$ (in this question whole mass is considered on centre of mass and hence for calculating max displacement, we are calculating he displacement of centre of mass only)
Question 9
1 / -0

Identical springs of steel and sopper $$(Y_s > Y_{cu})$$ are equally stretched. Then

A
less work is done on steel spring

B
less work is done on copper spring

C
equal work is done on both the springs

D
data not complete

Solution

$$Work=Force\times Displacement$$
Now, Displacement is given as: $$\Delta l=\dfrac{FL}{AY}$$ or, $$F=\dfrac{AY\Delta l}{L}$$
Thus, $$Work=\dfrac{AY{(\Delta l)}^{2}}{L}$$
Since, similar wires are used and extension is same, thus, A, $$\Delta l$$ and L are same. Also, $${Y}_{s}>{Y}_{Cu}$$.
Thus, work on steel is greater than work on copper.
Question 10
1 / -0

There are two wires of same material and same length while the diameter of second wire is two times the diameter of first wire, then the ratio of extension produced in the wires by applying same load will be

A
$$1:1$$

B
$$2:1$$

C
$$1:2$$

D
$$4:1$$

Solution

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Mechanical Properties of Solids Test - 35

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Mechanical Properties of Solids Test - 35

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Question 1

$$1.8$$

$$3.6$$

$$0.6$$

$$8.7$$

Solution

Question 2

Elongation is inversely proportional to length

Elongation is directly proportional to cross section $$A$$

Elongation is inversely proportional to $$A$$

Elongation is directly proportional to Young's module

Solution

Question 3

thin block of any cross section

thick block of any cross section

long thin wire

short thin wire

Solution

Question 4

Zero, as for elongation to be there, equal and opposite forces must act on the rod

Non-zero but cannot be determine from the given situation

$$4\mu m$$

$$16\mu m$$

Solution

Question 5

$$1.5mm$$

$$6mm$$

$$24mm$$

$$96mm$$

Solution

Question 6

There will be no change in the size of the bubbles

The bubbles will become of equal size

$$A$$ will become smaller and $$B$$ will become larger

The sizes of $$A$$ and $$B$$ will be interchanged

Solution

Question 7

$$3600$$

$$7200$$

$$10800$$

$$14400$$

Solution

Question 8

$$\displaystyle\frac{mgl}{2AY}$$

$$\displaystyle\frac{2mgl}{AY}$$

$$\displaystyle\frac{mgl}{AY}$$

$$\displaystyle\frac{mgY}{Al}$$

Solution

Question 9

less work is done on steel spring

less work is done on copper spring

equal work is done on both the springs

data not complete

Solution

Question 10

$$1:1$$

$$2:1$$

$$1:2$$

$$4:1$$

Solution

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