Young's Modulus of Elasticity

Q.

What is the modulus of elasticity of steel?

Q. Two point charges placed at a distance $r$ in air exert a force $F$ on each other. What will be the distance at which they will experience force $4F$, when placed in a medium of dielectric constant $16$?

1. $r$
2. $\frac{r}{4}$
3. $\frac{r}{8}$
4. $2r$

Q. Choose the correct relationship between Young's modulus $\left(Y\right)$, shear modulus $\left(G\right)$ and Poisson's ratio $\left(\mu \right)$.

1. $Y=2G(1-2\mu )$
2. $Y=2G(1-\mu )$
3. $Y=2G(1+2\mu )$
4. $Y=2G(1+\mu )$

Q. The following four wires (given in options) are made of the same material. Which of these will have the largest extension when the same load is applied?

1. Length $=50\text{cm}$, diameter $=0.5\text{mm}$
2. Length $=100\text{cm}$, diameter $=1\text{mm}$
3. Length $=200\text{cm}$, diameter $=2\text{mm}$
4. Length $=300\text{cm}$, diameter $=3\text{mm}$

Q.

In a Young’s double slit experiment, light of $500nm$ is used to produce an interference pattern. When the distance between the slits is$0.05mm$, the angular width (in degree) of the fringes formed on the distance screen is close to:

1. $0.17°$

2. $0.07°$

3. $0.57°$

4. $1.7°$

Q. A uniform slender rod of length L, cross sectional area A and Young’s modulus Y is acted upon by the forces shown in the figure. The elongation of the rod is

1. 
2. 
3. 
4. 

Q.

The unit of equivalent conductivity is

1. $\mathrm{S}{\mathrm{cm}}^{-2}$

2. $\mathrm{ohm}·{\mathrm{cm}}^2(\mathrm{g}-\mathrm{equivalent})$

3. $\mathrm{ohm}-\mathrm{cm}$

4. ${\mathrm{ohm}}^{-1}·{\mathrm{cm}}^2{(\mathrm{g}-\mathrm{equivalent})}^{-1}$

Q. Two wires are made of the same material and have the same volume. However, wire 1 has cross sectional area 3A. If length of wire 1 increased by x on applying force F, how much force is needed to stretch wire 2 by the same amount?

1. 6F
2. 9F
3. 4F
4. F

Q. White light is used to illuminate the two slits in YDSE. The separation between the slits is b and the screen is at a distance d (>>b) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are

1. $\lambda =\frac{b^2}{d}$
2. $\lambda =\frac{2b^2}{d}$
3. $\lambda =\frac{b^2}{3d}$
4. $\lambda =\frac{2b^2}{3d}$

Q. A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

1. 
2. 
3. 
4. 

Q. A large glass slab $(\mu =5/3)$ of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R?

Q. In a Young's double slit experiment, slits are separated by $0.5mm$, and the screen is placed $150cm$ away. A beam of light consisting of two wavelengths, $650nm$ and $520nm$, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is

1. $15.6mm$
2. $1.56mm$
3. $7.8mm$
4. $9.75mm$

Q. The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of

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

Q.

What are the factors affecting the modulus of elasticity?

Q. A uniform rod of mass $M$ and length $L$ is hanging from point $P$ as shown in the figure. Find the elongation in its length due to the self weight of the rod. The Young's modulus of elasticity of the rod is $Y$ and cross-sectional area of the rod is $A$.

1. $\frac{MgL}{3AY}$
2. $\frac{2MgL}{3AY}$
3. $\frac{2MgL}{AY}$
4. $\frac{MgL}{2AY}$

Q. The load versus elongation graph of four wires of equal length of the same material is shown in the figure. The line representing the thinnest wire is

1. $B$
2. $C$
3. $D$
4. $A$

Q. Copper of fixed volume $V$ is drawn into a wire of length $L$. When this wire is subjected to a constant force $F$, the extension produced in the wire is $\Delta L$. Which of the following graphs is a straight line?

1. $\Delta L$ versus $\frac{1}{L}$
2. $\Delta L$ versus $L^2$
3. $\Delta L$ versus $\frac{1}{L^2}$
4. $\Delta L$ versus $L$

Q. Choose the correct option.

1. All of the above are correct.
2. For perfect plastic material, there is no restoring force.
3. Young's modulus for a perfectly plastic body is zero.
4. Steel is more elastic than rubber.

Q. In Young's double slit experiment, the distance between the slits is reduced to half and the distance between the slit and the screen doubled. The fringe width

1. will become one fourth
2. will become half
3. will be doubled
4. will become four times

Q. According to Hook's law of elasticity, within the elastic limit, if stress is increased, then the ratio of stress to strain

1. remains constant
2. becomes zero
3. decreases
4. increases

Q. The Young’s modulus of brass and steel are $10\times {10}^{10}N{m}^{-2}and2\times {10}^{11}N{m}^{-2}$ respectively. A brass wire and a steel wire of the same length are extended by 1 mm under the same force. The radii of the brass and steel wires are $R_B$ and $R_s$ respectively. Then

1. 
2. 
3. 
4. 

Q. If in case $A$, elongation in wire of length $L$ is $\Delta L$, then for the same wire, elongation in case $B$ will be

1. $2\Delta L$
2. $\Delta L$
3. $4\Delta L$
4. $\frac{\Delta L}{2}$

Q. Two equal charges are placed at a separation of $1\text{m}$. What should be the magnitude of the charges so that the force between them equals the weight of a $50\text{kg}$ person ?
(Take $g=10{\text{m/s}}^2$)

1. $3\times {10}^{-4}C$
2. $2.3\times {10}^{-4}C$
3. $3.2\times {10}^{-4}C$
4. $5\times {10}^{-5}C$

Q. In double slit experiment the angular width of the fringes is 0.20° for the sodium light
$(\lambda =5890\stackrel{\circ }{A})$. In order to increase the angular width of the fringes by $10\%$, then necessary changes in the wavelength (in $\stackrel{\circ }{A}$) is increase of

Q. The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are Young's moduli of the materials, then

1. $Y_A=Y_B$
2. $Y_B=3Y_A$
3. $Y_A=3Y_B$
4. $Y_B=2Y_A$

Q. If $I_0$ is the intensity of the principle maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled ?

1. $2I_0$
2. $4I_0$
3. $I_0$
4. $\frac{I_0}{2}$

Q. The spring block system as shown in figure is in equilibrium. The string connecting blocks $A$ and $B$ is cut. The mass of all the three blocks is $m$ and spring constant of both the spring is $k$. The amplitude of resulting oscillation of block $A$ is

1. $\frac{mg}{k}$
2. $\frac{2mg}{k}$
3. $\frac{3mg}{k}$
4. $\frac{4mg}{k}$

Q. Q. Two springs have force constant K1 and K2 ( K1> K2). Each spring is extended by same force F. Ifthe elastic potential energy are E1 and E2 then E1/E2 is
K1/K2
K2/K1
✓(K1/K2)
✓(K2/K1)
​​​​​​

Q.

A wire of density $9\times {10}^{-3}kgc{m}^{-3}$ is stretched between two clamps $1m$ apart. The resulting strain in the wire is $4.9\times {10}^{-4}.$ The lowest frequency of the transverse vibrations in the wire is (Young’s modulus of wire $Y=9\times {10}^{10}N{m}^{-2}$), (to the nearest integer), _______.

Q. The Young's modulus of a rubber string 8 cm long and density 1.5 $\frac{kg}{m^3}$ is 5 $\times {10}^8\frac{N}{m^2}$. It is suspended from the ceiling in a room. The increase in length due to its own weight will be

1. 9.6 X 10^-5 m
2. 9.6 X 10^-11 m
3. 9.6 X 10^-3 m
4. 9.6 m