unit of universal gravitational constant is ............ (a) \(\mathrm{kg} \mathrm{m} \mathrm{sec}^{-1}\) (b) \(\mathrm{N} \mathrm{m}^{-1} \mathrm{sec}\) (c) \(\mathrm{N} \mathrm{m}^{2} \mathrm{~kg}^{-2}\) (d) \(\mathrm{N} \mathrm{m} \mathrm{kg}^{-1}\)

The formula for the gravitational force F, between two masses m1 and m2, separated by a distance r, is given by: \[F = G \frac{m_{1} m_{2}}{r^{2}}\] Here, G is the universal gravitational constant.

Before finding the units of the universal gravitational constant, we need to determine the dimensions of other quantities in the formula for gravitational force. The dimensions are: - F (gravitational force): Newtons (N) - m1 (mass of the first object): kilograms (kg) - m2 (mass of the second object): kilograms (kg) - r (distance between the two objects): meters (m)

Now, we need to rearrange the formula for gravitational force to isolate G: \[G = \frac{F r^{2}}{m_{1} m_{2}}\] Now, substitute the dimensions of the quantities: \[G = \frac{(\mathrm{N}) (\mathrm{m})^{2}}{(\mathrm{kg}) (\mathrm{kg})} = \frac{\mathrm{N} \mathrm{m}^{2}}{\mathrm{kg}^{2}}\] So, the unit of the universal gravitational constant G is Newton meter square per kilogram square (N m² kg⁻²). In our given options: (a) \(\mathrm{kg} \mathrm{m} \mathrm{sec}^{-1}\) (Incorrect) (b) \(\mathrm{N} \mathrm{m}^{-1} \mathrm{sec}\) (Incorrect) (c) \(\mathrm{N} \mathrm{m}^{2} \mathrm{~kg}^{-2}\) (Correct) (d) \(\mathrm{N} \mathrm{m} \mathrm{kg}^{-1}\) (Incorrect) Hence, the correct answer is: (c) \(\mathrm{N} \mathrm{m}^{2} \mathrm{~kg}^{-2}\)