Q89 / 125 · BITSAT 2014 · Physics

For the equation $\mathrm{F}=\mathrm{A}^{a} \mathrm{v}^{\mathrm{b}} \mathrm{d}^{\mathrm{c}},$ where $\mathrm{F}$ is the force, A is the area, $v$ is the velocity and d is the density, the values of $a, b$ and $c$ are respectively

  • Correct answer
    A
    1,2,1
  • B
    2,1,1
  • C
    1,1,2
  • D
    0,1,1

Solution

$\left[\mathrm{MLT}^{-2}\right]=\left[\mathrm{L}^{2 \mathrm{a}}\right] \times\left[\mathrm{L}^{\mathrm{b}} \mathrm{T}^{-\mathrm{b}}\right]\left[\mathrm{M}^{\mathrm{c}} \mathrm{L}^{-3 \mathrm{c}}\right]$ $$ =\left[\mathrm{M}^{\mathrm{c}} \mathrm{L}^{2 \mathrm{a}+\mathrm{b}-3 \mathrm{c}} \mathrm{T}^{-\mathrm{b}}\right] $$ Comparing powers of $\mathrm{M}, \mathrm{L}$ and $\mathrm{T},$ on both sides, we get $$ \begin{array}{l} \mathrm{c}=1,2 \mathrm{a}+\mathrm{b}-3 \mathrm{c}=1,-\mathrm{b}=-2 \text { or } \mathrm{b}=2 \\ \text { Also, } 2 \mathrm{a}+2-3(1)=1 \Rightarrow 2 \mathrm{a}=2 \text { or } \mathrm{a}=1 \end{array} $$ $\therefore$ This is 1,2,1

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

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