Question

Which of the following are dimensionless quantities,(symbols have their usual meaning)
[$\eta$=viscocity,$\rho$=density,$r$=radius,$k$=thermal conductivity,$c$=heat capacity.]

• A. $\frac{k}{\rho \times c}$
• B. $\frac{\rho \times v\times r}{\eta }$
• C. Specific gravity
• D. Rate of change of angle (in radians) of rotation.

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\frac{k}{\rho \times c}$
B $\frac{\rho \times v\times r}{\eta }$
C Specific gravity

The dimesnion of $k$ is $M^1{T}^1{L}^{-3}{\theta }^{-1}$

$\eta =M{L}^{-1}{T}^{-1}$

$c=L^{2}M{T}^{-2}{\theta }^{-1}$

$\rho =M{L}^{-3}$

$r=L$

Specific gravity is the ratio of the density of a substance to the density of a reference substance, so the specific gravity is dimensionless.

$\frac{k}{\rho \times c}=M^0{L}^0{T}^0$

$\frac{\rho \times v\times r}{\eta }=M^0{L}^0{T}^0$