Q. Dimensions of bulk modulus are
A) $\left\lbrack M^{- 1}{LT}^{- 2} \right\rbrack$
B) $\left\lbrack {ML}^{- 1}T^{- 2} \right\rbrack$
C) $\left\lbrack {ML}^{- 2}T^{- 2} \right\rbrack$
D) $\left\lbrack M^{2}L^{2}T^{- 1} \right\rbrack$
Explanation
$Bulk\ modulus\ K = \frac{normal\ stress}{volumetric\ strain}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{F/A}{- \mathrm{\Delta}V/V}$ $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = - \frac{FV}{A\ \mathrm{\Delta}V}$ Now, $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{F}{A} = p$ $\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K = \frac{pV}{\mathrm{\Delta}V}$ As volumetric strain is dimensionless. $\therefore Dimensions\ of\ K = dimensions\ of\ normal\ stress$ $\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lbrack K\rbrack = \left\lbrack ML^{- 1}T^{- 2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.