Question

any one plzz solve thiz ........​

Answer 1

Question :

Four identical masses of m are kept at the corners of a square of side a. Find the gravitational force exerted on one of the masses by the other masses.

Solution :

❖ The magnitude of gravitational force between two masses is directly proportional to the product of masses and inversely proportional to the square of the distance between them.

Mathematically,

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

This is known as newton's law of gravitation.

Let's find force exerted on first mass by the other three point masses.

$\sf:\implies\:F=F_{12}\:cos(45^{\circ})+F_{13}+F_{14}\:cos(45^{\circ})$

$\sf:\implies\:F=\dfrac{Gm_1m_2}{\sqrt2r_1^2}+\dfrac{Gm_1m_3}{r_2^2}+\dfrac{Gm_1m_4}{\sqrt2r_3^2}$

$\sf:\implies\:F=Gm^2\left[\dfrac{1}{\sqrt2a^2}+\dfrac{1}{(\sqrt2a)^2}+\dfrac{1}{\sqrt2a^2}\right]$

$\sf:\implies\:F=\dfrac{Gm^2}{a^2}\left[\dfrac{2}{\sqrt2}+\dfrac{1}{2}\right]$

$:\implies\:\underline{\boxed{\bf{\gray{F=\dfrac{Gm^2}{a^2}\left(\sqrt2+\dfrac{1}{2}\right)}}}}$