MCQ

MCQ 2011 Mark

A student plots a graph from his reading on the determination of Young's modulus of a metal wire but forgets to label. The quantities on $X$ and $Y$ axes may be respectively.

A
Weight hung and length increased
B
Stress applied and length increased
✓
Stress applied and strain developed
D
Length increased and weight hung

Answer

Correct option: C.

Stress applied and strain developed

(c)

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MCQ 2021 Mark

The diagram shows the change ${ }^x$ in the length of a thin uniform wire caused by the application of stress $F$ at two different temperatures $T$ and $T$. The variations shown suggest that

✓
$T_1>T_2$
B
$T_1
C
$T_1=T_2$
D
None of these

Answer

Correct option: A.

$T_1>T_2$

(a) Elasticity of wire decreases at high temperature i.e. at higher temperature slope of graph will be less.So we can say that $T_1>T_2$

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MCQ 2031 Mark

Which one of the following is the Young's modulus (in $N / m$ ) for the wire having the stress-strain curve shown in the figure

A
$24 \times 10^{11}$
B
$8.0 \times 10^{11}$
C
$10 \times 10^{11}$
✓
$2.0 \times 10^{11}$

Answer

Correct option: D.

$2.0 \times 10^{11}$

(d) Young's modulus is defined only in elastic region and
$Y=\frac{\text { Stress }}{\text { Strain }}=\frac{8 \times 10^7}{4 \times 10^{-4}}=2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2$

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MCQ 2041 Mark

The value of force constant between the applied elastic force $F$ and displacement will be

A
$\sqrt{3}$
✓
$\frac{1}{\sqrt{3}}$
C
$\frac{1}{2}$
D
$\frac{\sqrt{3}}{2}$

Answer

Correct option: B.

$\frac{1}{\sqrt{3}}$

(b) Force constant, $\mathrm{K}=\tan 30^{\circ}=1 / \sqrt{3}$

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MCQ 2051 Mark

The strain-stress curves of three wires of different materials are shown in the figure. $P, Q$ and $R$ are the elastic limits of the wires. The figure shows that

A
Elasticity of wire $P$ is maximum
B
Elasticity of wire $Q$ is maximum
C
Tensile strength of $R$ is maximum
✓
None of the above is true

Answer

Correct option: D.

None of the above is true

(d) As stress is shown on $x$-axis and strain on $y$-axisSo we can say that $Y=\cot \theta=\frac{1}{\tan \theta}=\frac{1}{\text { slope }}$So elasticity of wire $P$ is minimum and of wire $R$ is maximum

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MCQ 2061 Mark

In the above graph, point $D$ indicates

A
limiting point
B
Yield point
✓
Breaking point
D
None of the above

Answer

Correct option: C.

Breaking point

(c)

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MCQ 2071 Mark

In the above graph, point $B$ indicates

A
Breaking point
B
Limiting point
✓
Yield point
D
None of the above

Answer

Correct option: C.

Yield point

(c)

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MCQ 2081 Mark

A graph is shown between stress and strain for a metal. The part in which Hooke's law holds good is

✓
$O A$
B
$A B$
C
$B C$
D
$C D$

Answer

Correct option: A.

$O A$

(a) In the region $O A$, stress $\propto$ strain i.e. Hooke's law hold good.

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MCQ 2091 Mark

One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the roof and a weight $W_1$ is suspended from its lower end. If $S$ is the area of cross-section of the wire, the stress in the wire at a height $3 L / 4$ from its lower end is

A
$\frac{W_1}{S}$
B
$\frac{W_1+(W / 4)}{S}$
✓
$\frac{W_1+(3 W / 4)}{S}$
D
$\frac{W_1+W}{S}$

Answer

Correct option: C.

$\frac{W_1+(3 W / 4)}{S}$

(c) Total force at height $3 L / 4$ from its lower end$=$ Weight suspended + Weight of $3 / 4$ of the chain$=W_1+(3 W / 4)$Hence stress $=\frac{W_1+(3 W / 4)}{S}$

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MCQ 2101 Mark

Two rods of different materials having coefficients of linear expansion $\alpha_1, \alpha_2$ and Young's moduli $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If $\alpha_1: \alpha_2=2: 3$, the thermal stresses developed in the two rods are equally provided $Y_1: Y_2$ is equal to

A
$2: 3$
B
$1: 1$
✓
$3: 2$
D
$4: 9$

Answer

Correct option: C.

$3: 2$

(c) Thermal stress $=Y \alpha \Delta \theta$.If thermal stress and rise in temperature are equal then$Y \propto \frac{1}{\alpha} \Rightarrow \frac{Y_1}{Y_2}=\frac{\alpha_2}{\alpha_1}=\frac{3}{2}$

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MCQ 2111 Mark

Ametre $^2$ is suspended vertically. Density of rubber is $D$ $kg /$ metre $^3$ and Young's modulus of rubber is $E$ newton / metre ${ }^2$. If the wire extends by 1 metre under its own weight, then extension $l$ is

A
$L^2 D g / E$
✓
$L^2 D g / 2 E$
C
$L^2 D g / 4 E$
D
$L$

Answer

Correct option: B.

$L^2 D g / 2 E$

(b)

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MCQ 2121 Mark

For a constant hydraulic stress on an object, the fractional change in the object's volume $\left(\frac{\Delta V}{V}\right)$ and its bulk modulus $$ are related as

A
$\frac{\Delta V}{V} \propto B$
✓
$\frac{\Delta V}{V} \propto \frac{1}{B}$
C
$\frac{\Delta V}{V} \propto B^2$
D
$\frac{\Delta V}{V} \propto B^{-2}$

Answer

Correct option: B.

$\frac{\Delta V}{V} \propto \frac{1}{B}$

(b) $B=\frac{\Delta p}{\Delta V / V} \Rightarrow \frac{1}{B} \propto \frac{\Delta V}{V} \quad[\Delta p=$ constant $]$

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MCQ 2131 Mark

The pressure of a medium is changed from $1.01 \times 10$ Pa to $1.165 \times 10$ $P a$ and change in volume is $10 \%$ keeping temperature constant. The Bulk modulus of the medium is

A
$204.8 \times 10^5\ pa$
B
$ 102.4 \times 10^5\ pa$
C
$51.2 \times 10^5\ pa$
✓
$1.55 \times 10^5\ pa$

Answer

Correct option: D.

$1.55 \times 10^5\ pa$

$ K=\frac{\Delta p}{\Delta V / V}=\frac{(1.165-1.01) \times 10^5}{10 / 100}=\frac{0.155 \times 10^5}{1 / 10} $
$ =1.55 \times 10^5\ pa$

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MCQ 2141 Mark

The pressure applied from all directions on a cube is $P$. How much its temperature should be raised to maintain the original volume ? The volume elasticity of the cube is $\beta$ and the coefficient of volume expansion is $\alpha$

✓
$\frac{P}{\alpha \beta}$
B
$\frac{P \alpha}{\beta}$
C
$\frac{P \beta}{\alpha}$
D
$\frac{\alpha \beta}{P}$

Answer

Correct option: A.

$\frac{P}{\alpha \beta}$

(a) If coefficient of volume expansion is $\alpha$ and rise in temperature is $\Delta \theta$ then $\Delta V=V \alpha \Delta \theta$
$\Rightarrow \frac{\Delta V}{V}=\alpha \Delta \theta$ Volume elasticity
$\beta=\frac{P}{\Delta V / V}=\frac{P}{\alpha \Delta \theta} \Rightarrow \Delta \theta=\frac{P}{\alpha \beta}$

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MCQ 2151 Mark

In the three states of matter, the elastic coefficient can be

A
Young's modulus
✓
Coefficient of volume elasticity
C
Modulus of rigidity
D
Poisson's ratio

Answer

Correct option: B.

Coefficient of volume elasticity

(b)

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MCQ 2161 Mark

The compressibility of a material is

A
Product of volume and its pressure
✓
The change in pressure per unit change in volume strain
C
The fractional change in volume per unit change in pressure
D
None of the above

Answer

Correct option: B.

The change in pressure per unit change in volume strain

The fractional change in volume per unit change in pressure

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MCQ 2171 Mark

If the volume of the given mass of a gas is increased four times, the temperature is raised from $27^{\circ} C$ to $127^{\circ} C$. The elasticity will become

A
$4$ times
B
$1/4$ times
C
$3$ times
✓
$1/3$ times

Answer

Correct option: D.

$1/3$ times

From the ideal gas equation $\frac{P_1 V_1}{T_1}=\frac{P_2 V_2}{T_2}$
$\frac{E_2}{E_1}=\frac{P_2}{P_1}=\frac{V_1}{V_2} \times \frac{T_2}{T_1}=\left(\frac{1}{4}\right) \times\left(\frac{400}{300}\right)=\frac{1}{3} \Rightarrow E_2=\frac{E_1}{3}$
i.e. elasticity will become $\frac{1}{3}$ times.

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JEE physics MCQ