Question

Please explain why in the last sentence “newton (meter)” upon “kilogram” is squared.

Answer 1

Explanation:

The SI unit of universal gravitation constant is Nm²/kg². Let's see how.

As we know that,

$\longrightarrow \boxed{\tt { G = F \times \dfrac{r^2}{m_1 \times m_2} }}$

Now, write the SI units of the physical quantities in RHS.

• SI unit of force is N (Newton).
• SI unit of mass is kg (kilograms).
• SI unit of radius which is the form of length is m (metre).

$\longrightarrow \tt { Unit_{(G)} = N \times \dfrac{(m)^2}{kg \times kg} }$

Square of m is m² and kg × kg can be written as kg².

$\longrightarrow \tt { Unit_{(G)} = N \times \dfrac{m^2}{kg^2} }$

Rearrange the terms.

$\longrightarrow \tt { Unit_{(G)} = \dfrac{N(m^2)}{kg^2} }$

Performing the multiplication.

$\longrightarrow \underline{ \boxed{\tt { Unit_{(G)} = \dfrac{Nm^2}{kg^2} }}} \; \bigstar$

In this way, the SI unit of universal gravitation constant is Nm²/kg² and that's why metre and kilograms are squared.