What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 10²⁴ kg and radius of the earth is 6.4 × 10⁶ m.)

Mass of the body (m) = 1 kg

Mass of the earth (M) = 6 × 10²⁴ kg

Radius of the Earth (R) = 6.4 × 10⁶ m

G = 6.67 x 10^-11 Nm²kg^-2

According to the formula for gravitational force we know,

F = G $\dfrac{\text{M}\text{m}}{\text{R}^2}$

Substituting we get,

$\text{F} = \dfrac{6.67 \times 10^{-11}\times 6 \times 10^{24} \times 1}{(6.4 \times 10^6)^2} \\[1em] = \dfrac{6.67 \times 10^{13}}{6.4 \times 6.4 \times10^{12}} \\[1em] = 9.77 \text{ N} \approx 9.8 \text{ N}$

Hence, magnitude of the gravitational force = 9.8 N