If the dimensions of a physical quantity are given by $\left[\mathrm{M}^{\mathrm{a}} \mathrm{L}^{\mathrm{b}}…

If the dimensions of a physical quantity are given by $\left[\mathrm{M}^{\mathrm{a}} \mathrm{L}^{\mathrm{b}} \mathrm{T}^{\mathrm{c}}\right]$, then the physical quantity will be :
  1. Force if $a=0, b=-1, c=-2$
  2. Pressure if $\mathrm{a}=1, \mathrm{~b}=-1, \mathrm{c}=-2$
  3. Velocity if $a=1, b=0, c=-1$
  4. Acceleration if $a=1, b=1, c=-2$

Solution

$[\mathrm{P}]=\frac{\mathrm{F}}{\mathrm{A}}=\left[\frac{\mathrm{MLT}^{-2}}{\mathrm{~L}^2}\right]=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$

Asked in: NEET 2009 (Mains)

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