Mechanical Properties of Solids Test

Result

Mechanical Properties of Solids Test - 55

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

A metal rod of Young's modulus $$Y$$ and coefficient of thermal expansion $$\alpha$$ is held at its two ends such that its length remains invariant. If its temperature is raised by $${t}^{o}C$$, the linear stress developed in it is:

A
$$1/\left( Y\alpha t \right) $$

B
$$\alpha t/Y$$

C
$$Y/\alpha t$$

D
$$Y\alpha T$$

Solution
Question 2
1 / -0

For which material the poisson's ratio is greater than 1

A
Steel

B
Copper

C
Aluminium

D
None of the above

Solution

Poisson's ratio can lie only between 0 to 1. It cannot be greater than 1 for any material

The correct option is (d)
Question 3
1 / -0

The maximum strain energy that can be stored in a body is known as:

A
impact energy

B
toughness

C
proof resilience

D
none of the above

Solution

Proof resilience is defined as the maximum energy that can be absorbed up to the elastic limit, without creating a permanent distortion.
Question 4
1 / -0

The proportional limit of steel is $$8\times { 10 }^{ 8 }N/{ m }^{ 2 }$$ and its Young's modulus is $$2\times { 10 }^{ 11 }N/{ m }^{ 2 }$$. The maximum elongation, a one metre long steel wire can be given without exceeding the proportional limit is

A
2 mm

B
4 mm

C
1 mm

D
8 mm

Solution

The correct option is B

Given,

Proportional limits of steel are $$8\times10^8N/m^2$$

Young's modulus is $$2\times10^{11}N/m^2$$

So, Stress up to which stress and strain are proportional.

So $$\dfrac{stress}{strain}=\dfrac{8\times10^8}{strain}$$

Since

$$ strain = \dfrac{stress}{modulus}$$

$$\Rightarrow strain=\dfrac{4\times10^8}{2\times10^{11}}$$

$$=4\times10^{-3}$$

Thus,

$$\dfrac{\Delta L}{L}=4\times10^{-3}$$ Where $$\Delta L$$ is stress

But, $$L=1m$$

So,

$$\Delta L=4\times10^{-3}m$$

$$=4mm$$
Question 5
1 / -0

A rubber ball is taken to depth $$1$$ km inside water so that its volume reduces by $$0.05\% $$.What is the bulk modulus of the rubber:

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

B
$$2 \times {10^{9\,}}\,N/{m^2}$$

C
$$2 \times 10^{7}N/m^2$$

D
$$2 \times {10^{11\,}}\,N/{m^2}$$

Solution

Pressure at $$1\ km$$ depth inside water,

$$P=1000\times 10\times 1000=10^7\ Nm^{_2}$$

say, V=volume of ball

$$\dfrac{0.05}{100}\times V$$ = Reduction in volume (i.e) $$\Delta V$$

Bulk Modulus, $$\beta=\dfrac{-PV}{\Delta V}=\dfrac{-10^7\times V}{\dfrac{-0.05V}{100}}$$

$$=2\times 10^{10}\ Nm^{-2}$$

Hence Option $$\textbf A $$ is correct.
Question 6
1 / -0

Select the correct alternative(s).

A
Elastic forces are always conservative

B
Elastic forces are not always conservative

C
Elastic forces are conservative only when Hooke's law is obeyed

D
Elastic forces may be conservative even when Hooke's law is not obeyed

Solution

Elastic forces are conservative because work done in closed path is always zero. Take a spring energy gets stored when we compress it and again becomes zero if we release the net work done in the cycle is zero.
Question 7
1 / -0

Overall changes in volume and radii of a uniform cylindrical steel sire are $$0.2\%$$ and $$0.002\%$$ respectively when subjected to some suitable force. Longitudinal tensile stress acting on the wire is :-
$$(Y=2.0\times 10^{11}\ NM^{-2})$$

A
$$3.2\times 10^{9}\ Nm^{-2}$$

B
$$3.2\times 10^{7}\ Nm^{-2}$$

C
$$3.6\times 10^{9}\ Nm^{-2}$$

D
$$3.9\times 10^{8}\ Nm^{-2}$$

Solution
Question 8
1 / -0

When the load on a wire is increasing slowly from $$2$$ kg to $$4$$ kg, the elongation increases from $$0.6$$ mm to $$1$$ mm. The work done during this extension of the wire is $$(g=10 m/s^2)$$.

A
$$14\times 10^{-3}$$J

B
$$0.4\times 10^{-3}$$J

C
$$8\times 10^{-2}$$J

D
$$10^{-3}$$J

Solution

$$W=(\dfrac{1}{2}F_2\times \Delta l_2)-(\dfrac{1}{2}F_1\times \Delta l_1)=20\times 10^{-3}=6\times 10^{-3}=14\times 10^{-3}$$J
Hence (A) is correct.
Question 9
1 / -0

What is the percentage increase in length of a wire of diamater $$2.5\ mm$$, stretched by a force of $$100\ Kg\ wt$$? Youngs modulus of elasticity of wire $$=1.25 \times {10}^{11}\ dyne/{cm}^{2}$$

A
$$0.16\%$$

B
$$0.32\%$$

C
$$0.08\%$$

D
$$0.12\%$$

Solution
Question 10
1 / -0

A steel wire has length 2.0 m, radius 1 mm and $$Y = 2 \times 10^{11} N/m^2$$ A sphere of mass 1 kg is attached at one end of the wire which is then whirled in a vertical circle with speed 2 rev/sec. Elongation of the wire when mass is at the lowest position.

A
1.0 mm

B
2.0 mm

C
0.1 mm

D
0.01 mm

Solution

$$ \begin{array}{l} \text { Given, lure of length }=2 \mathrm{~m} \\ \text { radius }=1 \mathrm{~mm} \\ y=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2} \\ \text { sphere of mass }=1 \mathrm{~kg} \\ \text { frequency }=2 \end{array} $$
$$ \begin{aligned} T-m g &=m \omega^{2} R \\ T=& m g+m \omega^{2} R \\ =& 10+16 \pi^{2}(2) \\ &=325 N \\ T=& Y A\left(\frac{\Delta L}{L}\right) \\ \frac{325 \times(2)}{2 \times 10^{11} \times \pi\left(10^{-6}\right)} &=\Delta L \\ \therefore & \Delta L=1 \mathrm{~mm} \end{aligned} $$

User

Question Analysis

Correct -
Wrong -
Skipped -

My Perfomance

Score
-
out of -
Rank
-
out of -

Re-Attempt Weekly Quiz Competition

Mechanical Properties of Solids Test - 55

Result

Mechanical Properties of Solids Test - 55

Score

-

Rank

-

SHARING IS CARING

Question 1

$$1/\left( Y\alpha t \right) $$

$$\alpha t/Y$$

$$Y/\alpha t$$

$$Y\alpha T$$

Solution

Question 2

Steel

Copper

Aluminium

None of the above

Solution

Question 3

impact energy

toughness

proof resilience

none of the above

Solution

Question 4

2 mm

4 mm

1 mm

8 mm

Solution

Question 5

$$2 \times 10^{10} N/m^2$$

$$2 \times {10^{9\,}}\,N/{m^2}$$

$$2 \times 10^{7}N/m^2$$

$$2 \times {10^{11\,}}\,N/{m^2}$$

Solution

Question 6

Elastic forces are always conservative

Elastic forces are not always conservative

Elastic forces are conservative only when Hooke's law is obeyed

Elastic forces may be conservative even when Hooke's law is not obeyed

Solution

Question 7

$$3.2\times 10^{9}\ Nm^{-2}$$

$$3.2\times 10^{7}\ Nm^{-2}$$

$$3.6\times 10^{9}\ Nm^{-2}$$

$$3.9\times 10^{8}\ Nm^{-2}$$

Solution

Question 8

$$14\times 10^{-3}$$J

$$0.4\times 10^{-3}$$J

$$8\times 10^{-2}$$J

$$10^{-3}$$J

Solution

Question 9

$$0.16\%$$

$$0.32\%$$

$$0.08\%$$

$$0.12\%$$

Solution

Question 10

1.0 mm

2.0 mm

0.1 mm

0.01 mm

Solution

User

Question Analysis

My Perfomance

Score

-

Rank

-

Results Announcement on: coming Monday

Stay Tuned: We’ll update you on your result via email or SMS.