An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is
An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is
- [IIT 1992]
- [AIIMS 1997]
- [AIEEE 2005]
- A
$\frac{{2Y}}{{{S^2}}}$
- B
$\frac{{{S^2}}}{{2Y}}$
- C
$\frac{S}{{2Y}}$
- D
$\frac{{{S^2}}}{Y}$
Similar Questions
The diameter of a brass rod is 4 mm and Young's modulus of brass is $9 \times {10^{10}}\,N/{m^2}$. The force required to stretch by $0.1\%$ of its length is
The diameter of a brass rod is 4 mm and Young's modulus of brass is $9 \times {10^{10}}\,N/{m^2}$. The force required to stretch by $0.1\%$ of its length is
A rubber cord $10\, m$ long is suspended vertically. How much does it stretch under its own weight $($Density of rubber is $1500\, kg/m^3, Y = 5×10^8 N/m^2, g = 10 m/s^2$$)$
A rubber cord $10\, m$ long is suspended vertically. How much does it stretch under its own weight $($Density of rubber is $1500\, kg/m^3, Y = 5×10^8 N/m^2, g = 10 m/s^2$$)$
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.
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.
A rod of uniform cross-sectional area $A$ and length $L$ has a weight $W$. It is suspended vertically from a fixed support. If Young's modulus for rod is $Y$, then elongation produced in rod is ......
A rod of uniform cross-sectional area $A$ and length $L$ has a weight $W$. It is suspended vertically from a fixed support. If Young's modulus for rod is $Y$, then elongation produced in rod is ......
$A$ rod of length $1000\, mm$ and coefficient of linear expansion $a = 10^{-4}$ per degree is placed symmetrically between fixed walls separated by $1001\, mm$. The Young’s modulus of the rod is $10^{11} N/m^2$. If the temperature is increased by $20^o C$, then the stress developed in the rod is ........... $MPa$
$A$ rod of length $1000\, mm$ and coefficient of linear expansion $a = 10^{-4}$ per degree is placed symmetrically between fixed walls separated by $1001\, mm$. The Young’s modulus of the rod is $10^{11} N/m^2$. If the temperature is increased by $20^o C$, then the stress developed in the rod is ........... $MPa$