Q166 / 180 · COMEDK 2018 · Physics

Dimensional formula for the universal gravitational constant $G$ is

  • A
    $\left[\mathrm{M}^{-1} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]$
  • B
    $\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]$
  • Correct answer
    C
    $\left[\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-2}\right]$
  • D
    $\left[\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-1}\right]$

Solution

According to Newton's law of gravitation, $$ F=\frac{G m_{1} m_{2}}{r^{2}} $$ where, $F$ = gravitational force between two bodies of masses $m_{1}$ and $m_{2}$, $r=$ distance between the two masses and $G=$ universal gravitational constant. $\therefore \quad G=\frac{F r^{2}}{m_{1} m_{2}} .$ $\therefore \quad[G]=\frac{[F]\left[r^{2}\right]}{\left[m_{1}\right]\left[m_{2}\right]}$ $=\frac{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{L}^{2}\right]}{[\mathrm{M}][\mathrm{M}]}=\left[\mathrm{M}^{-1} \mathrm{~L}^{3} \mathrm{~T}^{-2}\right]$

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

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