Question

Which of the following physical quantities represent the dimensions of $\frac{b}{a}$ in the relation $P=\frac{x^2-b}{at}$, where $P$ is power, $x$ is distance and $t$ is time.

• A. Power
• B. Surface tension
• C. Torsional constant
• D. Force

Answer 1

The correct option is C Torsional constant

Dimension of $b$ must be $L^2$.

Dimension of $P$ is $M^1{L}^2{T}^{-3}$.

$\left[at\right]=\frac{L^2}{M^1{L}^2{T}^{-3}}\Rightarrow \left[a\right]=M^{-1}{L}^0{T}^2\left[\frac{b}{a}\right]=M^1{L}^2{T}^{-2}$

which is same as torsional constant.