The unit of the universal gravitational constant should be N·m2/kg2, not Nmkg-2. Dimensional analysis confirms that the printed document is incorrect because it omits the square on the meter, which is essential for calculating the force in newtons (N).
The unit of the universal gravitational constant (G) given as Nmkg-2 needs to be checked for its correctness using dimensional analysis. The correct units for G, according to Newton's law of universal gravitation, are N·m2/kg2. In other words, G should have the units N·m2/kg2 (newton meter squared per kilogram squared) in SI units. To understand this, we can look at the formula for gravitational force (F) which is F = G·(Mm/r2), where M and m are the masses of the objects and r is the distance between them. Since force (F) is measured in newtons (N), and considering that N is equivalent to kg·m/s2, we can deduce that the units of G must combine with M and m (both in kg) and r2 (in m2) to produce a result in newtons. Therefore, G should have the units of N·m2/kg2, which can be further understood as kg·m/s2·m2/kg2.
This confirms that the printed document is incorrect in presenting G as having units of Nmkg-2 because it lacks the square on the meter (m), which is necessary for the units to cancel out properly and provide a force in newtons as per the equation.