Gravitational field due to left over part of a uniform sphere from which a part has shown has been removed out at a very far off. Be located as shown would be nearly
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first of all, we have to find mass of small part.
mass of small part = mass density of big sphere × volume of small part
or, m = M/(4/3 πR³) × 4/3π(R/2)³ = M/8
gravitational field due to rest part = gravitational field due to big sphere - gravitational small part
= GM/X² - Gm/(R/2 + X)²
= GM/X² - GM/8(R/2 + X)²
= GM [ 1/X² - 1/8(R/2 + X)²]
for vary far point , X > > R/2
so, (R/2 + X) ≈ X
so, Gravitational field due to rest part = GM[1/X² - 1/8X² ]
= 7GM/8X²
mass of small part = mass density of big sphere × volume of small part
or, m = M/(4/3 πR³) × 4/3π(R/2)³ = M/8
gravitational field due to rest part = gravitational field due to big sphere - gravitational small part
= GM/X² - Gm/(R/2 + X)²
= GM/X² - GM/8(R/2 + X)²
= GM [ 1/X² - 1/8(R/2 + X)²]
for vary far point , X > > R/2
so, (R/2 + X) ≈ X
so, Gravitational field due to rest part = GM[1/X² - 1/8X² ]
= 7GM/8X²
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