Longitudinal Stress

Q.

How does the modulus of elasticity change with temperature?

Q.

What is plastic moment of resistance?

Q.

Why is the modulus of elasticity of steel is greater than that of rubber under the same stress?

Q.

What is a high modulus of elasticity?

Q.

A transverse wave travels on a taut steel wire with a velocity of$𝑉$ when tension in it is $2.06\times {10}^4𝑁$. When the tension is changed to$T$, the velocity changed to $\frac{V}{2}$ The value of $T$ is close to

1. $30.5\times {10}^4$

2. $2.50\times {10}^4$

3. $10.2\times {10}^2$

4. $5.15\times {10}^3$

Q. Breaking force depends upon the area of the section of the wire for a given material.

1. True
2. False

Q.

A rope 1 cm in diameter breaks if the tension in it exceeds 500N. The maximum tension that may be given to a similar rope of diameter 2 cm is?

1. 500 N

2. 250 N

3. 1000 N

4. 2000 N

Q. A mass of $100\text{gram}$ is attached to the end of a rubber string $49\text{cm}$ long having an area of cross-section $20{\text{mm}}^2$. The string is whirled around horizontally at a constant speed of $40\text{rps}$ in a circle of radius $51\text{cm}$. Find the ratio of longitudinal stress and longitudinal strain in the rubber string.

1. $3{\pi }^2\times {10}^9{\text{Nm}}^{-2}$
2. $4{\pi }^2\times {10}^9{\text{Nm}}^{-2}$
3. $4{\pi }^2\times {10}^8{\text{Nm}}^{-2}$
4. $6{\pi }^2\times {10}^8{\text{Nm}}^{-2}$

Q.

One end of a uniform rod of mass M and cross-sectional area A is suspended from a rigid support and an equal mass M is suspended from the other end. The stress at the mid-point of the rod will be

1. $\frac{2Mg}{A}$

2. $\frac{3Mg}{2A}$

3. $\frac{Mg}{A}$

4. Zero

Q. The breaking stress of the metal used for the wire connecting the blocks is $2\times {10}^9{\text{N/m}}^2$. Minimum radius of the wire is:
[Take $\sqrt{\frac{400}{6\pi }}=4.60,g=10{\text{m/s}}^2$ for calculation.]

1. $4.6\times {10}^{-5}\text{m}$
2. $9.6\times {10}^{-5}\text{m}$
3. $8.6\times {10}^{-5}\text{m}$
4. $5.6\times {10}^{-5}\text{m}$

Q. The maximum stress that can be applied to the material of a wire used to suspend an elevator is ${10}^8{\text{Nm}}^{-2}$. If the mass of the elevator is $1000\text{kg}$ and it moves up with an acceleration of $0.2{\text{ms}}^{-2}$, what is the minimum diameter of the wire required? (Take $g=9.8\text{m}/{\text{s}}^2$)

1. $2\times \frac{{10}^{-2}}{\sqrt{\pi }}\text{m}$
2. $\frac{{10}^{-2}}{\sqrt{\pi }}\text{m}$
3. $2\times \frac{{10}^{-2}}{\sqrt{2\pi }}\text{m}$
4. $4\times {10}^{-2}\text{m}$

Q. Stress is a vector quantity.

1. False
2. True

Q. 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 $3L/4$ from its lower end is

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

Q. A man grows into a giant such that his linear dimensions increases by a factor of $9$. If his density remains same, then stress on the leg will increase by a factor of
(Assume cubical shape of man with $L$ as edge length).

Q.

Two blocks of masses 1 kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in figure. The breaking stress of the metal is $2\times {10}^{9}N{m}^{-2}$. What should be the minimum radius of the wire used if it is not to break? Take $g=10m{s}^{-2}$.

1. $2.3\times {10}^{-5}m$

2. $4.6\times {10}^{-4}m$

3. $4.6\times {10}^{-5}m$

4. $2.3\times {10}^{-4}m$

Q. Modulus of elasticity of a material does not depend upon

1. impurities mixed
2. stress
3. nature of material
4. temperature

Q. A $4.0\text{m}$ long copper wire of cross sectional area $1.2{\text{cm}}^2$ is stretched by a force of $4.8\times {10}^3\text{N}$. The stress will be

1. $4.0\times {10}^7{\text{N/mm}}^2$
2. $4.0\times {10}^7{\text{KN/m}}^2$
3. $4.0\times {10}^7{\text{N/m}}^2$
4. None of these

Q. The ratio of radii of two wires of same material is $3:1$. If these wires are stretched by equal force, the ratio of stresses produced in them is

1. $1:3$
2. $3:1$
3. $9:1$
4. $1:9$

Q. A two metre long rod is suspended with the help of two wires of equal length. One wire is of steel and its cross-sectional area is $0.1c{m}^2$ and another wire is of brass and its cross-sectional area is $0.2c{m}^2$. If a load W is suspended from the rod and stress produced in both the wires is same then the ratio of tensions in them will be

1. Will depend on the position of W
2. $\frac{T_1}{T_2}=2$
3. $\frac{T_1}{T_2}=1$
4. $\frac{T_1}{T_2}=0.5$

Q. A $4.0\text{m}$ long copper wire of cross sectional area $1.2{\text{cm}}^2$ is stretched by a force of $4.8\times {10}^3\text{N}$. The stress will be

1. $4.0\times {10}^7{\text{N/mm}}^2$
2. $4.0\times {10}^7{\text{KN/m}}^2$
3. $4.0\times {10}^7{\text{N/m}}^2$
4. None of these

Q. The wires $A$ and $B$ shown in the figure are made of the same material and have radii $r_A$ and $r_B$, respectively. The block between them has a mass $m$. When the force $F$ is $mg/3$, one of the wires breaks. Then,

1. $A$ will break before $B$ if $r_A=r_B$.
2. $A$ will break before $B$ if $r_A<2r_B$.
3. either $A$ or $B$ may break if$r_A=2r_B$.
4. the lengths of $A$ and $B$ must be known to predict which wire will break.

Q. A rope 1 cm in diameter breaks at a tension of 500 N. A similar rope of diameter 2 cm can bear a tension of

1. 500 N
2. 250 N
3. 1000 N
4. 2000 N

Q. A mass of $100\text{gram}$ is attached to the end of a rubber string $49\text{cm}$ long having an area of cross-section $20{\text{mm}}^2$. The string is whirled around horizontally at a constant speed of $40\text{rps}$ in a circle of radius $51\text{cm}$. Find the ratio of longitudinal stress and longitudinal strain in the rubber string.

1. $3{\pi }^2\times {10}^9{\text{Nm}}^{-2}$
2. $4{\pi }^2\times {10}^9{\text{Nm}}^{-2}$
3. $4{\pi }^2\times {10}^8{\text{Nm}}^{-2}$
4. $6{\pi }^2\times {10}^8{\text{Nm}}^{-2}$

Q. Stress generated in a wire when force $F_1$ acts on it as shown in the figure, is $T$. Initial cross sectional area of the wire is $A_1$. When force $F_2$ replaces $F_1$, cross-sectional area becomes $A_2$. Find $\left(\frac{A_2}{A_1}\right)$ if $F_2=6\text{N}$.
[Consider stress generated in the wire to be the same]

1. $3$
2. $1/2$
3. $4$
4. $1/6$

Q.

A bar of cross-section A is subjected to two equal and opposite tensile forces at its ends. Consider a plane section of the bar whose normal makes an angle θ with the axis of the bar.

·What is the tensile stress on this plane?

·What is the shearing stress on this plane?

1. $\frac{F}{A}co{s}^2\theta ,\frac{Fsin\theta cos\theta }{A}$

2. $\frac{F}{A}si{n}^2\theta ,\frac{F}{A}co{s}^2\theta$

3. $\frac{F}{A}si{n}^2\theta ,\frac{Fsin\theta cos\theta }{A}$

4. $\frac{F}{A}co{s}^2\theta ,\frac{F}{A}si{n}^2\theta$

Q. A and B are two wires. The radius of A is twice that of B. they are stretched by the same load. Then the stress on B is

1. Equal to that on A
2. Four times that on A
3. Two times that on A
4. Half that on A

Q. A 5 m long aluminium wire $(Y=7\times {10}^{10}N/m^2)$ of diameter 3 mm supports a 40 kg mass. In order to have the same elongation in a copper wire $(Y=12\times {10}^{10}N/m^2)$ of the same length under the same weight, the diameter should now be, in mm

1. 1.75
2. 2
3. 2.3
4. 5

Q. Two rods $A$ and $B$, each of equal length but different materials are suspended from a common support as shown in the figure. The rods $A$ and $B$ can support a maximum load of $W_1=600\text{N}$ and $W_2=6000\text{N}$ respectively. If their cross-sectional areas are $A_1=10{\text{mm}}^2$ and $A_2=1000{\text{mm}}^2$, respectively, then the stronger material is:

1. Material $A$
2. Material $B$
3. Both have same strength
4. Cannot comment

Q.

A metal bar of length L and area of cross-section A is rigidly clamped between two walls. The Young's modulus of its material is Y and the coefficient of linear expansion is $\alpha$. The bar is heated so that its temperature increases by ${\theta }^{\circ }C$. The force exerted at the ends of the bar is given by

1. $YL\alpha \theta$

2. $YL\alpha \frac{\theta }{A}$

3. $YA\alpha \theta$

4. $Y\theta \alpha \frac{L}{A}$

Q. A bar is subjected to equal and opposite forces as shown in the figure. PQRS is a plane making angle $\theta$ with the cross-section of the bar. If the area of cross-section be ‘A’, then what is the tensile stress on PQRS

1. $\frac{F}{A}$
   
2. $\frac{Fcos\theta }{A}$
   
3. $\frac{Fco{s}^2\theta }{A}$
   
4. $\frac{F}{Acos\theta }$