Which of the following pairs of physical quantities possess same dimension?
Which of the following pairs of physical quantities possess same dimension?
Force and surface tension
Frequency and velocity gradient
Angular speed and solid angle
Stefan's constant and Planck's constant
Solution
We know that, the dimension formula of given physical quantities are
$[$ Force $]=\left[\mathrm{MLT}^2\right]$
[Surface tension] $=\left[\mathrm{ML}^0 \mathrm{~T}^{-2}\right]$
$[$ Frequency $]=\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-1}\right]$
[Velocity gradient $]=\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-1}\right]$
[Angular speed] $=\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^{-1}\right]$
[Solid angle] $=\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^0\right]$
[Stefan's constant] $=\left[\mathrm{ML}^0 \mathrm{~T}^{-3} \mathrm{~K}^{-4}\right]$
and [Planck's constant $]=\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$
Hence, we found that only (frequency and velocity gradient) pair has same dimensions.