Question

what is the magnitude of the gravitation force between the earth and a 1kg object on it's surface?
(mass of the earth is 6 × 10^24 kg and radius of the earth is 6.4 × 10^6 m). ​

Answer 1

Given :

Mass of the object = 1kg

Mass of the earth = 6 × 10²⁴ Kg

Radius of the earth = 6.4 × 10⁶ m

To find :

The magnitude of the gravitation force between the earth and the object.

Solution :

According to the universal law of gravitation,

» The force of attraction between two particles is proportional to the product of their masses and inversely proportional to the square of the distance between them .i.e.,

$\underline{ \boxed{ {\bf F = \dfrac{Gm_1m_2}{r^2}}}}$

where,

• G is the gravitational constant, G = 6.7 × 10¯¹¹ Nm²/kg²
• m₁ denotes mass of the object
• m₂ denotes mass of the earth
• r denotes radius of the earth

by substituting all the given values in the equation,

$\leadsto\bf F = \dfrac{Gm_1m_2}{r^2}$

$\leadsto\bf F = \dfrac{6.7 \times {10}^{ - 11} \times 6 \times {10}^{24} \times 1}{(6.4 \times 10^6) ^{2} }$

$\leadsto \bf F = 9.8 \: N$

Thus, the gravitational force between the earth and the object is 9.8 N.