If the velocity of the shear wave through a soil deposit is determined as $V_s$, the shear modulus 'G' is given as: (where, $\rho =$ mass density of soil)
Show Hint
- $\rho V$
- $\dfrac{\rho}{V_s}$
- $\rho V_s^2$
- $(\rho V_s)^{1/2}$
The Correct Option is C
Solution and Explanation
Step 1: Recall formula for shear modulus.
Shear modulus is related to shear wave velocity as:
\[
G = \rho V_s^2
\]
Step 2: Explanation.
- $V_s = \sqrt{\dfrac{G}{\rho}}$ (wave velocity formula)
- Rearranging gives $G = \rho V_s^2$.
Step 3: Conclusion.
Thus, the correct formula is $\rho V_s^2$.
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