Longitudinal Stress

Q.

A student performs an experiment to determine Young’s modulus of a wire, exactly $2m$ long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be $0.8mm$ with an uncertainty of $\pm 0.05mm$ at a load of exactly $1.0kg$. The student also measures the diameter of the wire to be $0.4mm$ with an uncertainty of $\pm 0.01mm$. Take $g=9.8m{s}^{-2}$ (exact). The Young’s modulus obtained from the reading is

1. $\left(2.0\pm 0.3\right)\times {10}^{11}N{m}^{-2}$

2. $\left(2.0\pm 0.2\right)\times {10}^{11}N{m}^{-2}$

3. $\left(2.0\pm 0.1\right)\times {10}^{11}N{m}^{-2}$

4. $\left(2.0\pm 0.05\right)\times {10}^{11}N{m}^{-2}$

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 $3L/5$ from its lower end is

1. $W_1/S$
2. $(W_1+\frac{2W}{5})S$
3. $\frac{(W_1+\frac{3W}{5})}{S}$
4. $(W_1+W)S$

Q. What is mean by dimensional homogeneity?

Q. Wires \(W_{1}\) and \(W_{2}\) are made of same material having the breaking stress of \(1.25\times 10^{9}\text{ N/m}^{2}. W_{1}~\text{and}~W_{2}\) have cross-sectional area of \(8\times 10^{-7}~\text m^{2}~\text{and}~ 4\times 10^{-7}~\text m^{2}, \) respectively. Masses of \(20~\text {kg}\) and \(10~\text{kg}\) hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is

\(\text{kg}\). (Use \(g=10\text{ m/s}^{2}\))
\( w_{1} \) \( 20 kg \) \( 10 kg \) pan

Q. The ratio of radii of two wires of the same material is $2:1$. If these wires are stretched by equal forces, then the ratio of stresses produced in them will be

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

Q. Which of the following quantities has the same unit as pressure?

1. Strain
2. Stress
3. Torque
4. Momentum

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

Q. Stress is a vector quantity.

1. False
2. True

Q.

A cubical box is to be constructed with iron sheets 1 mm in thickness. What can be the minimum value of the external edge so that the cube does not sink in water ? Density of iron = 8000 kg $m^{-3}$ and density of water = 1000 kg $m^{-3}$.

Q.

How do you calculate simple interest in months?

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.

A 2m long light metal rod AB is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One wire is of brass and has cross section of $0.2\times {10}^{-4}{m}^2$ and the other is of steel with $0.1\times {10}^{-4}{m}^2$ cross section. In order to have equal stress in the two wires, a weight is hang from the rod. The position of the weight along the rod from end A should be.

1. 44.4 cm

2. 155.6 cm

3. 66.6 cm

4. 133 cm

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

Q. The maximum load that a wire can withstand without breaking, when its length is reduced to half of its original length, will .

1. become double
2. remain same
3. become half

Q.

A chapati maker is a machine which converts balls of dough into chapati. What effect of force comes into play in this process?

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. 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. 
   
2. 
   
3. 
4. 
   

Q. At a given instant, $A$ is moving with velocity of $5m/s$ upwards. What is velocity of $B$ at that time ?

1. $15m/s\downarrow$
2. $15m/s\uparrow$
3. $5m/s\downarrow$
4. $5m/s\uparrow$

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.

What is a resistant body?

Q.

A ceiling fan has a diameter (of the circle through the outer edges of the three blades) of 120 cm and rpm 1500 at full speed. Consider a particle of mass 1 g sticking at the outer end of a blade. How much force does it experience when the fan runs at full speed ? Who exerts this force on the particle? How much force does the particle exert on the blade along its surface?

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

Q. A uniform steel rod of density $\rho$, cross - sectional area $A$ and length $L$ is suspended so that it hangs vertically. The stress at the middle point of the rod is given by $\frac{\rho gL}{N}$. Then, the value of $N$ is

Q. A brass rod is to support a load of $400\text{N}$. If its elastic limit is $4.0\times {10}^8{\text{N/m}}^2$, its minimum diameter must be :

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

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. What is the minimum height $\left(\text{in}\text{m}\right)$ of a brick column of uniform cross section for which column breaks due to its own weight. $[P_{\text{atmospheric}}=100\text{kPa},\rho =1.8\times {10}^3{\text{kg/m}}^3$, Breaking stress $\sigma =3.7\text{MPa}]$

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 wire can be broken by a load of $20\mathrm{kg}-\mathrm{wt}$. The force required to break wire of same material with twice the diameter will be

1. $5\mathrm{kg}-\mathrm{wt}$

2. $80\mathrm{kg}-\mathrm{wt}$

3. $20\mathrm{kg}-\mathrm{wt}$

4. $160\mathrm{kg}-\mathrm{wt}$

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. A uniform rod of mass $6kg$ is lying on a smooth horizontal surface. Its two ends are pulled by strings as shown in figure. Force exerted by $40cm$ part of the rod on $10cm$ part of the rod is

1. $30N$
2. $16N$
3. $24N$
4. $22N$