Q160 / 200 · Manipal (MET) 2010 · Physics

If force is proportional to square of velocity, then the dimensions of proportionality constant is

  • A
    $\left[\mathrm{ML}^{-1} \mathrm{~T}\right]$
  • Correct answer
    B
    $\left[\mathrm{ML}^{-1} \mathrm{~T}^0\right]$
  • C
    $\left[\mathrm{MLT}^0\right]$
  • D
    $\left[\mathrm{M}^0 \mathrm{LT}^{-1}\right]$

Solution

As $F \propto v^2$ or $F=k v^2$ $\therefore k=\frac{F}{v^2}$ $[k]=\frac{[F]}{\left[v^2\right]}=\frac{\left[\mathrm{MLT}^{-2}\right]}{\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]}$ $=\left[\mathrm{ML}^{-1} \mathrm{~T}^0\right]$

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

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