Q: It is proposed to define newton (N) as the force between two masses of 1 kg each separated by a distance of 1 m. what would be the value of gravitational constant G ?

(a) 100 Nm^{2} kg^{-2}

(b) 10 Nm^{2} kg^^{-2}

(c) 1000 Nm^{2} kg^{-2}

(d) 1 Nm^{2} kg^{-2}

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Ans: (d)

Sol: $\displaystyle F = G \frac{m_1 m_2}{r^2} $

$\displaystyle G = \frac{F r^2}{m_1 m_2} $

$\displaystyle G = \frac{1 N \times (1 m)^2}{1 kg \times 1 kg} $

G = 1 Nm^{2} kg^{-2}