Q105 / 150 · MHT CET 2020 (12 Oct Shift 1) · Physics

If the dimensions of a physical quantity are given by $\left[\mathrm{L}^{\mathrm{a}} \mathrm{M}^{\mathrm{b}} \mathrm{T}^{c}\right]$ then the physical quantity is

  • A
    velocity if $a=-1, b=0, c=+1$
  • B
    force if $a=-1, b=1, c=-2$
  • Correct answer
    C
    pressure if $a=-1, b=1, c=-2$
  • D
    acceleration if $\mathrm{a}=1, \mathrm{~b}=1, \mathrm{c}=-2$

Solution

A. pressure if $a=1, b=-1, c=2$ Dimensions of velocity $=\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-1}\right]$ Here, $a=0, b=1, c=-1$ Dimension of acceleration $=\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]$ Dimension of force $=\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]$ Dimension of pressure $=\left[\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\right.$ The physical quantity is pressure.

Hence, the correct answer is option: 'C'.

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