GATE-2018 (24) :Wyllie – Time average equation

GATE 2019

25. The shear wave velocity in an igneous rock with a density of 2.7 g/cc and rigidity modulus of 24.3 GPa is ___________ km/s(round off to 1 decimal point)
(Thanks to Neeraja AU)

Sol: Shear wave velocity ,

$V_s=\sqrt{\frac{\mu}{\rho}}--(1)$

$\mu - rigidity modulus$

$\mu = 24.3GPa=24.3\times10^9Pa$

$\rho-density$

$\rho=2.7g/cc=2700kg/m^3$

Substitute above values in equation(1) 

$V_s=\sqrt{\frac{24.3\times10^9}{2700}}$

$V_s=\sqrt{9000000}$

$V_s=3000m/s$

$V_s=3km/s$

Unit Conversion:

$Pascal=\frac{Force}{Area}=\frac{mass\times acceleration}{Area}=\frac{kg\times m/s^2}{m^2}$

$density=\frac{mass}{volume}=\frac{kg}{m^3}$

$\therefore \frac{Pascal}{density}=\frac{kg\times m/s^2\times m^3}{m^2\times kg}=m^2/s^2$