Question

The mass of earth is 6x1024 kg and that of the moon is 7.4x 1022kg. If the distance between the earth and the moon is 3.84x105km. Calculate the force exerted by the earth and the moon. 2 G=6.67x10-11 Nm2 kg-2

Answer 1

⇒ Correct Question:

The mass of the Earth is 6 x 10²⁴ kg and that of the moon is 7.4 x 10²². If the distance between the earth and the moon is 3.84 x 10⁵ km, calculate the force exerted by the Earth on the moon. [G = 6.67 x 10⁻¹¹ Nm²/kg²]

⇒ Given:

The mass of the Earth = 6 x 10²⁴ kg

The mass of the moon = 7.4 x 10²²

Distance between the Earth and the moon = 3.84 x 10⁵ km

Gravitational constant [G] = 6.67 x 10⁻¹¹ Nm²/kg²

⇒ To Find:

The force exerted by the Earth on the moon.

⇒ Formula to be used:

→ $\boxed{\sf{\dfrac{F=GMm}{R^2}}}$

⇒ Solution:

Mass of the Earth [M] = 6 x 10²⁴ kg

Mass of the moon [m] = 7.4 x 10²² kg

Gravitational constant [G] =  6.67 x 10⁻¹¹ Nm²/kg²

Distance between the Earth and the moon [R] = 3.84 x 10⁵ km i.e  3.84 x 10⁵ x 1000 m

= 3.84 x 10⁸ m

Substituting the given values in the formula:

$\sf{F=\dfrac{6.67\times10^{-11}\times6\times10^{24}\times7.4\times10^22}{(3.84\times10^8)^2}}$

$\sf{F=\dfrac{6.67\times6\times7.4\times10^{-11+24+22}}{3.84^2\times10^{16}}}$

$\sf{F=\dfrac{297.48\times10^{35}}{14.7456\times10^{16}}}$

$\sf{F=20.17\times10^{19}}$

This can be written as:

$\sf{F=2.017\times10^{20}N}$

Hence the force exerted by the Earth on the Moon is 2.017 x 10²⁰N.

The Universal Law of Gravitation:

Every object in the universe attracts every other object in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.