Mechanical Properties of Solids Test

Result

Mechanical Properties of Solids Test - 82

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 uniform metal wire ring of mass per unit length $$\lambda$$ and radius $$r$$ has cross sectional area $$S$$.
If $$Y$$ is Young's in modulus of elasticity and it is rotated with and angular velocity $$\omega$$ about it own axis then approximate fractional change in radius is

A
$$\left( \dfrac{\lambda r^{2} \omega^{2}}{SY} -1 \right)$$

B
$$\dfrac{\lambda r^{2} \omega^{2}}{SY}$$

C
$$1-\dfrac{\lambda r^{2} \omega^{2}}{SY}$$

D
$$\dfrac{\lambda r \omega^{2}}{SY}$$
Question 2
1 / -0

A steel rod of cross sectional area $$1 m^2$$ is acted upon by forces shown in the fig. Determine the total elongation of the bar. ($$Y = 2.0 \times 10^{11} N/m^2$$)

A
$$10 \times 10^{-7}$$

B
$$13 \times 10^{-7}$$

C
$$23 \times 10^{-7}$$

D
none

Solution
Question 3
1 / -0

What force should be applied to the ends of steel rod of a cross sectional area $$10 { cm } ^ { 2 }$$ to prevent it from elongation when heated from $$273 { K }$$ to $$303 { K }$$ ? ( $$\alpha$$ of steel $$10^{ { -5 } }\quad ^{ 0 }{ { C }^{ -1 } },Y=2\times 10^{ { 11 } }{ Nm }^{ { -2 } }$$ )

A
$$2\times 10^{ { 4 } }{ N }$$

B
$$3\times 10^{ { 4 } }{ N }$$

C
$$6\times 10^{ { 4 } }{ N }$$

D
$$12\times 10^{ { 4 } }{ N }$$

Solution
Question 4
1 / -0

In the young's double slit experiments, the intensities at two points $$ P_1 $$ and $$ P_2 $$ on the screen are respectively.$$ I_1 $$ and $$ I_2 $$. If $$ P_1 $$ is located at the centre of a bright fringe and $$ P_2 $$ is located at a distance equal to a quarter of fringe width from $$ P_1$$, then $$ \frac {I_1}{I_2} $$ is

A
2

B
3

C
4

D
none of these

Solution

$$\begin{array}{l}\text { Given, } \\\text { } P_{1} \text { and } P_{2} \text { are two points on screen and } \\\text I_{ 1 } { and } I_{2}\text { are their intensities respectively. } \\\text {} P_{2} \text { is located at quarter of fringe width }\end{array}$$
$$Y_{p_{2}}=\frac{\beta}{4}, \beta=\text { fringe width }$$
$$y_{p_{2}}=\frac{\lambda D}{4 d}$$
$$\begin{array}{c}\text { and } p_{1} \text { is located at centre of bright fringe } \\\qquad y_{p_{1}}=0\end{array}$$
$$\begin{array}{l}\text { now, } \\\qquad\begin{aligned}\frac{Y_{2} d}{D} &=\frac{\lambda}{4} \\\Delta x_{p_{2}} &=\frac{\lambda}{4}\end{aligned}\end{array}$$
$$\begin{aligned}\text { Now, }\\\text { phase difference }(\phi) &=\frac{2 \pi}{\lambda}\times\text { Path difterence } \\&=\frac{2 \pi}{\lambda} \times \frac{\lambda}{4}\\\phi_{P_{2}} &=\frac{\pi}{2}\end{aligned}$$
$$\text { So, }\begin{aligned}I_{2} &=4 I_{0} \cos ^{2}\left(\frac{\phi}{2}\right) \\&=4 I_{0} \cos ^{2}(45) \\I_{2} &=\frac{4 I_{0}}{2}\end{aligned}$$
$$\text { Now for } P_{1} \text { as it lies at centre of fringe }$$
$$\begin{aligned} & \phi_{p_{1}}=0 \\ I_{1} &=4 I_{0} \cos ^{2}(0) \\ I_{1} &=4 I_{0} \\ \text { Now, } & \frac{I_{1}}{I_{2}}=\frac{4 I_{0}}{2 I_{0}}=2 \end{aligned}$$
Question 5
1 / -0

If uniform rod of length $$5 { m },$$ area of cross-section $$50{ cm }^{ { 2 } }$$ and Young's modulus $$4 \times 10 ^ { 9 } { Pa }$$ is lying at rest under the action of forces as shown, then the total extension in the rod is

A
$$1.5\times 10^{ { -2 } }{ m }$$

B
$$10 ^ { - 1 } { m }$$

C
$$2 \times 10 ^ { - 2 } { m }$$

D
$$5 \times 10 ^ { - 2 } { m }$$

Solution
Question 6
1 / -0

In the question $$22$$, when is the tensile stress maximum ?

A
$$\theta =0^0$$

B
$$\theta =30^0$$

C
$$\theta =45^0$$

D
$$\theta =90^0$$
Question 7
1 / -0

A uniform steel rod of length 1m and area of cross section 20 $$ c{ m }^{2 } $$ is hanging from a fixed support. Find the increase in the length of the rod.
$$ ({ Y}_{ steel }=2.0\times 1{0 }^{ 11 }N{m }^{ -2 }, {P }_{ steel }= 7.85\times 1{0 }^{ 3 }kg{m }^{-3 }) $$

A
$$1.923\times 1{ 0 }^{ -5 }cm $$

B
$$ 2.923\times 1{ 0 }^{ -5 }cm $$

C
$$ 1.123\times 1{ 0 }^{ -5 }cm $$

D
$$ 3.123\times 1{ 0 }^{ -5 }cm $$

Solution
Question 8
1 / -0

A uniform wire fixed at its upper end hangs vertically and supports a weight at its lower end. If its radius is r, length is L and the Young's modulus for the material of the wire is E then extension produced in the wire is

A
directly proportional to E

B
inversely proportional to r

C
directly proportional to L

D
all of these

Solution
Question 9
1 / -0

A steel wire of length 4 m and diameter 5 mm is stretched by 5 kgwt. The increase in its length , if the Young's modulus of steel wire is $$2.4 \times { 10 }^{ 12 } dyne/{ cm }^{ 2 }$$. is

A
0.003 cm

B
0.0042 cm

C
0.00042 cm

D
0.005 cm

Solution
Question 10
1 / -0

A body of mass 10 kg is attached to a 0.3 m long wire of cross area $${ 10 }^{ 6 }$$ $${ m }^{ 2 }$$ Breaking steers of the wire if $$4.8\times { 10 }^{ 7 }$$ What is the maximum angular velocity with which it can be rotated in a horizontal circle?

A
4 rad/s

B
8 rad/s

C
16 rad/s

D
12 rad/s

Solution