The relation between $\gamma ,\,\eta $ and $K$ for a elastic material is
Diffcult
Download our app for free and get startedPlay store
$\mu=$ Modulus of Rigiditg

$k =$ Bulk Modulus.

$\sigma=$ Normal stress

$y =3 k (1-2 \sigma)-(1)$

$y =2 \eta(1+\alpha)-(2)$

$\frac{ y }{3 k }=1-2 \sigma-(3), \frac{ x }{2 \mu}=1+\sigma-(4)$

Multiply eq $4$ by $2$.

$\frac{ y }{3 k }+\frac{ y }{\mu}=3-(5)$

Adding equ" $(3)$ and eqn $(5)$

$\frac{ y }{3 k }+\frac{ y }{\mu}=3$

$\frac{1}{3 k }+\frac{1}{\mu}=\frac{3}{ y }$

$\frac{1}{ y }=\frac{1}{9 k }+\frac{1}{3 \mu}$

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
    An increases in pressure required to decreases the $200$ litres volume of a liquid by $0.004\%$ in container is .......... $kPa$ (Bulk modulus of the liquid $= 2100\, MPa$)
    View Solution
  • 2
    When a block of mass $M$ is suspended by a long wire of length $L$, the length of the wire become $(L+l) .$ The elastic potential energy stoped in the extended wire is :
    View Solution
  • 3
    A metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter $14\,mm$. The tensile stress developed in the wire under equilibrium state is $7 \times 10^5\,Nm ^{-2}$. The value of mass $m$ is $......kg$.

    (Take, $g =9.8\,ms ^{-2}$ and $\left.\pi=\frac{22}{7}\right)$

    View Solution
  • 4
    The Young's modulus of a wire is $Y.$ If the energy per unit volume is $E$, then the strain will be
    View Solution
  • 5
    The spring balance does not read properly after its long use, because
    View Solution
  • 6
    The length of wire becomes $l_1$ and $l_2$ when $100\,N$ and $120\,N$ tensions are applied respectively. If $10l_2=11l_1$, the natural length of wire will be $\frac{1}{x} l_1$. Here the value of $x$ is ........
    View Solution
  • 7
    In $CGS$ system, the Young's modulus of a steel wire is $2 \times {10^{12}}$. To double the length of a wire of unit cross-section area, the force required is
    View Solution
  • 8
    The load versus elongation graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line
    View Solution
  • 9
    Two wires $A$ and $B$ of same length, same area of cross-section having the same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of $A$ is $3/2$ times of that of wire $B$. The ratio of the forces produced in two wires will be
    View Solution
  • 10
    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