Choose the correct relationship between Poisson ratio $(\sigma)$. bulk modulus $( K )$ and modulus of rigidity $(\eta)$ of a given solid object:
JEE MAIN 2023, Medium
Download our app for free and get startedPlay store
$Y =3 \eta(1+\sigma)$

$Y =3 K (1-\sigma)$

$\Rightarrow 2 \eta(1+\sigma)=3 K (1-2 \sigma)$

$\Rightarrow \sigma=\left(\frac{3 K -2 \eta}{6 K +2 \eta}\right)$

art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    When the temperature of a gas is $20^{\circ} C$ and pressure is changed from $P_1=1.01 \times 10^5 \,Pa$ to $P_2=1.165 \times$ $10^5 \,Pa$, then the volume changes by $10 \%$. The Bulk modulus is .........$\times 10^5 \,Pa$
    View Solution
  • 2
    When a rubber ball is taken to the bottom of a sea of depth $1400 \,m$, its volume decreases by $2 \%$. The Bulk modulus of rubber ball is .................. $\times 10^8 N / m ^2$ [density of water is $1 \,g cc$ and $g=10 \,m / s ^2$ ]
    View Solution
  • 3
    The Poisson's ratio of a material is $0.5$. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by $4 \%$. The percentage increase in the length is ........ $\%$
    View Solution
  • 4
    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
    View Solution
  • 5
    The upper end of a wire of radius $4\, mm$ and length $100\, cm$ is clamped and its other end is twisted through an angle of $60^o$. Then angle of shear is .......... $^o$
    View Solution
  • 6
    A wire can be broken by applying a load of $20\,\,kg$  weight. The force required to break the wire of twice the diameter is ......... $kg\,wt$
    View Solution
  • 7
    The Young's modulus of a rubber string $8\, cm$ long and density $1.5\,kg/{m^3}$ is $5 \times {10^8}\,N/{m^2}$, is suspended on the ceiling in a room. The increase in length due to its own weight will be
    View Solution
  • 8
    A metal wire of length $'L'$ is suspended vertically from a rigid support. When a body  of mass $M$ is attached to the lower end of wire, the elongation in wire is $'l'$, consider the following statements 

    $(I)$  the loss of gravitational potential energy of mass $M$ is $Mgl$

    $(II)$ the elastic potential energy stored in the wire is $Mgl$

    $(III)$ the elastic potential energy stored in wire is $\frac{1}{2}\, Mg l$

    $(IV)$ heat produced is $\frac{1}{2}\, Mg l$ 

    Correct statement are :-

    View Solution
  • 9
    A string of area of cross-section $4\,mm ^{2}$ and length $0.5$ is connected with a rigid body of mass $2\,kg$. The body is rotated in a vertical circular path of radius $0.5\,m$. The body acquires a speed of $5\,m / s$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is $\ldots . . \times 10^{-5}$. (Use Young's modulus $10^{11}\,N / m ^{2}$ and $g =10\,m / s ^{2}$ )
    View Solution
  • 10
    A solid cube of copper of edge $10 \,cm$ subjected to a hydraulic pressure of $7 \times 10^6\, pascal$. If Bulk modulus of copper is $140 \,GPa$, then contraction in its volume will be ................ $m ^3$
    View Solution