Shear Modulus

Q.

What is modulus of rigidity?

Q.

Give Reason: We cannot go to the center of the Earth

Q.

Read the following two statements below carefully and state, with reasons, if it is true or false.

(a) The Young’s modulus of rubber is greater than that of steel;

(b) The stretching of a coil is determined by its shear modulus.

Q. The materials which have the same elastic properties in all directions are called

1. Elastic
2. Brittle
3. Ductile
4. Isotropic

Q.

What are the properties of viscosity?

Q. Why the maximum height of a mountain on Earth is ~10km?

Q.

what is pure torsion?

Q. 20.In a meter bridge experiment, when a nichrome wire is in the right gap, the balancing length is 60cm. When the nichrome wire is uniformly stretched to increase its length by 20% and again connected in the right gap, the new balancing length is nearly.

Q. A rubber cube of side $5\text{cm}$ has one side fixed while a tangential force equal to $1800\text{N}$ is applied to the opposite face. Find the shearing strain and the lateral displacement of the strained face. Modulus of rigidity for rubber is $2.4\times {10}^6{\text{N/m}}^2$.

1. $0.72\text{radian},1.96\text{cm}$
2. $0.3\text{radian},1.5\text{cm}$
3. $1.2\text{radian},1.225\text{cm}$
4. $0.98\text{radian},2.25\text{cm}$

Q. A rod of length $L$ having uniform cross-section area A is subjected to a tensile force P as shown in the figure below. If the Young's modulus of the material varies linearly from $E_1$ to $E_2$ along the length of the rod, the normal stress developed at the section-SS

1. $\frac{P}{A}$
   
2. $\frac{P(E_1-E_2)}{A(E_1+E_2)}$
   
   
3. $\frac{P{E}_2}{A{E}_1}$
   
4. $\frac{P{E}_1}{A{E}_2}$
   

Q. What is a horizontal force?

Q. In steel, the young’s modulus and the strain at the breaking point are $2\times {10}^{11}N/m^2$ and $0.15$, respectively. The stress at the break point for steel is

1. $1.33\times {10}^{-12}N/m^2$
2. $1.33\times {10}^{11}N/m^2$
   
3. $7.5\times {10}^{-3}N/m^2$
4. $3.0\times {10}^{10}N/m^2$

Q. The strain energy stored in a body of volume $V$ due to shear strain $\varphi$ is (shear modulus is $G$)

1. $\frac{{\varphi }^{2}V}{2G}$
2. $\frac{G\varphi V^2}{2}$
3. $\frac{\varphi V}{2G}$
4. $\frac{1}{2}G{\varphi }^{2}V$

Q. Which of the following factors is included in the limit state of strength?

1. Fire
2. Failure by excessive deformation
3. Corrosion
4. Repairable damage or crack due to fatigue

Q. What will be the modulus of rigidity for water, considering it to be ideal fluid ?

1. $\infty$
2. $0$
3. $1$
4. $-0.75$

Q. The Young’s modulus for steel is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress?

Q. Shear modulus is zero for

1. solids
2. liquids
3. gases
4. liquids and gases

Q.

Fill in the blanks using the word(s) from the list appended with each statement:

(a) Surface tension of liquids generally . . . with temperatures (increases / decreases)

(b) Viscosity of gases. .. with temperature, whereas viscosity of liquids . . . with temperature (increases / decreases)

(c) For solids with elastic modulus of rigidity, the shearing force is proportional to . . . , while for fluids it is proportional to . .. (shear strain / rate of shear strain)

(d) For a fluid in a steady flow, the increase in flow speed at a constriction follows (conservation of mass / Bernoulli’s principle)

(e) For the model of a plane in a wind tunnel, turbulence occurs at a ... speed for turbulence for an actual plane (greater / smaller)

Q. A cube of green jelly rests on a table. A lateral force of $30\text{N}$ is applied and the jelly tilts as shown in the figure. Choose the correct option(s).

1. Shear strain induced is $1.25$
2. Shear modulus is $1511.11{\text{N/m}}^2$
3. Shear strain induced is $0.58$
4. Shear modulus is $1111.11{\text{N/m}}^2$

Q.

What is the mechanical advantage and velocity ratio of the second class lever?

Q. Two wires A and B of same length and of the same material have the respective radii $r_1$ and $r_2$. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be

1. 
2. 
3. 
4. 

Q. Explain how the maximum height of mountain on earth can be estimated from elastic behaviour of earth

Q. A steel plate of upper face area $2{\text{cm}}^2$ and thickness $6\text{cm}$ is fixed rigidly at the lower surface. A tangential force $F=20\text{kN}$ is applied on the upper surface as shown in the figure. The lateral displacement $x$ of upper surface w.r.t the lower surface is (Take modulus of rigidity for steel is $8\times {10}^{11}{\text{N/m}}^2$).

1. $30\times {10}^{-6}\text{m}$
2. $7.5\times {10}^{-6}\text{m}$
3. $3.5\times {10}^{-6}\text{m}$
4. $15\times {10}^{-6}\text{m}$

Q. One of the square faces of a metal slab of side $50\text{cm}$ and thickness $20\text{cm}$ is rigidly fixed on a horizontal surface. If a tangential force of $30\text{N}$ is applied to the top face, then the displacement (in $\text{m}$) of the top face is :
[The shear modulus of the material is $4\times {10}^{10}{\text{N/m}}^2$]

1. $4\times {10}^{-12}$
2. $4\times {10}^{-10}$
3. $6\times {10}^{-10}$
4. $8\times {10}^{-10}$

Q.

in modulus of elasticity or modulus of rigidity what is the meaning of modulus?

Q. A cube of sponge rubber with edge length $5\text{cm}$ has a force of $2\text{N}$ applied horizontally to the top face (parallel to an edge) while the bottom face is held fixed. If the top face is displaced horizontally through a distance of $1\text{mm}$, find the shear modulus for the sponge rubber.

1. $4\times {10}^4{\text{N/m}}^2$
2. $8\times {10}^4{\text{N/m}}^2$
3. $24\times {10}^4{\text{N/m}}^2$
4. $32\times {10}^4{\text{N/m}}^2$

Q. A lead bar of length $50\text{cm}$ and square cross-section of side $5\text{cm}$ is fixed to a vertical wall as shown in figure. A massless tank is suspended from the end of the bar with the help of a massless rope. The tank is slowly filled with mercury at room temperature. Find the level of mercury in the tank so that the end of the bar deviates by $1\text{mm}$.
[Take modulus of rigidity for lead as $5.6\text{Gpa}$ and area of base of cylindrical tank as $0.42{\text{m}}^2;{\rho }_{Hg}=13600{\text{kg/m}}^3\&g=9.8{\text{m/s}}^2$]

1. $0.21\text{m}$
2. $0.42\text{m}$
3. $0.5\text{m}$
4. $1\text{m}$

Q. Shear modulus is zero for

1. solids
2. liquids
3. gases
4. liquids and gases

Q. The pressure that has to be applied to the ends of a steel wire of length $10cm$ to keep its length constant when its temperature is raised by 100${}^o$C is:
(For steel Young's modulus is $2\times {10}^{11}N{m}^{-2}$ and coefficient of thermal expansion is $1.1\times {10}^{-5}{K}^{-1}$)

1. $2.2\times {10}^7$Pa
2. $2.2\times {10}^6$Pa
3. $2.2\times {10}^8$Pa
4. $2.2\times {10}^9$Pa

Q. A cube of green jelly rests on a table. A lateral force of $30\text{N}$ is applied and the jelly tilts as shown in the figure. Choose the correct option(s).

1. Shear strain induced is $1.25$
2. Shear modulus is $1511.11{\text{N/m}}^2$
3. Shear strain induced is $0.58$
4. Shear modulus is $1111.11{\text{N/m}}^2$