Young's modulus, bulk modulus and modulus of rigidity — NEET & JEE Questions

Question 1 · difficulty L1 · recall

Young's modulus is defined as the ratio of

• A. longitudinal stress to longitudinal strain
• B. volume stress to volume strain
• C. shearing stress to shearing strain
• D. force to area only

Question 2 · difficulty L2 · understanding

Which elastic modulus relates pressure change to fractional change in volume?

• A. Young's modulus
• B. Bulk modulus
• C. Modulus of rigidity
• D. Poisson's ratio

Question 3 · difficulty L2 · understanding

The modulus of rigidity is associated primarily with

• A. change in length under normal stress
• B. change in volume under pressure
• C. change in shape under tangential stress
• D. thermal expansion

Question 4 · difficulty L2 · understanding

What is the SI unit common to Young's modulus, bulk modulus and modulus of rigidity?

• A. pascal
• B. newton
• C. joule
• D. metre

Question 5 · difficulty L3 · application

A wire of length $2.0\,\text{m}$ and cross-sectional area $1.0\times10^{-6}\,\text{m}^2$ extends by $1.0\,\text{mm}$ under a force of $100\,\text{N}$. What is its Young's modulus?

• A. $2.0\times10^8\,\text{Pa}$
• B. $2.0\times10^{10}\,\text{Pa}$
• C. $2.0\times10^{11}\,\text{Pa}$
• D. $2.0\times10^{12}\,\text{Pa}$

Question 6 · difficulty L3 · application

A material has bulk modulus $2.0\times10^9\,\text{Pa}$. If it is subjected to an increase in pressure of $1.0\times10^7\,\text{Pa}$, what is the magnitude of its fractional decrease in volume?

• A. 0.0005
• B. 0.005
• C. 0.05
• D. 0.5

Question 7 · difficulty L3 · application

A block experiences a tangential stress of $3.0\times10^6\,\text{Pa}$ and a shearing strain of $1.5\times10^{-3}$. What is its modulus of rigidity?

• A. $2.0\times10^6\,\text{Pa}$
• B. $2.0\times10^8\,\text{Pa}$
• C. $2.0\times10^9\,\text{Pa}$
• D. $4.5\times10^9\,\text{Pa}$

Question 8 · difficulty L3 · application

Two wires of the same material and length have radii $r$ and $2r$. The same tensile force is applied to each within the elastic limit. What is the ratio of their extensions $\Delta L_r:\Delta L_{2r}$?

• A. 1:2
• B. 1:4
• C. 2:1
• D. 4:1

Question 9 · difficulty L4 · application

A wire is stretched by a force $F$. If both its length and radius are doubled, while the same force is applied and the material is unchanged, how does its extension change?

• A. It becomes twice
• B. It becomes half
• C. It becomes one-fourth
• D. It remains unchanged

Question 10 · difficulty L4 · application

A cube is subjected to uniform pressure on all its faces. Which elastic modulus is needed to relate the pressure to its fractional change in volume?

• A. Young's modulus because all dimensions change
• B. Bulk modulus because the stress is hydrostatic
• C. Modulus of rigidity because the shape may change
• D. No modulus is required