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In short, explain the three moduli of elasticity by giving the equations.

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Young's Modulus(Y):- It is defined as the ratio of longitudinal stress to longitudinal strain.

$Y=\frac{longitudinal\ stress}{longitudinal\ strain}=\frac{F/A}{\Delta L/L}=\frac{Fl}{A\Delta L}$

Shear Modulus or Modulus of rigidity(G):- It is defined as the ratio of shearing stress to the shearing strain.

$G=\frac{shearing\ stress}{shearing\ strain}=\frac{F/A}{x/L}=\frac{Fl}{Ax}=\frac{F}{A\phi}$

Bulk Modulus(B):- It is defined as the ratio of volume stress to the volume strain.

$Volume stress=\frac{F}{A}=Pressure$

$B=-\frac{P}{\Delta V/V}$

The negative sign indicates that with the increase in pressure, volume decreases by $\Delta V$

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