two spheres of radius r and 2r made of same material are touching each other. the force of attraction between them is proportional to?
Answers
the force of attraction between them is directly proportional to r⁴.
Let density of each sphere is ρ
at first we have to find out mass of each sphere .
Volume of sphere of radius r , V₁ = 4/3 πr³
volume of sphere of radius 2r, V₂ = 4/3 π(2r)³ = 32πr³/3
Now, mass of 1st sphere, M₁ = V₁ × ρ [ mass = density × volume ]
= 4πr³ρ/3
mass of 2nd sphere, M₂ = V₂ × ρ = 32πr³ρ/3
Now, Gravitational force act between M₁ and M₂ , F = GM₁M₂/(r + 2r)²
= G {4πr³ρ/3}{32πr³ρ/3}/9r²
= 128π²r⁶ρ²/81r²
= 128π²r⁴ρ²/81
= (128π²ρ²/81)r⁴
i.e., F ∝ r⁴
here it is clear that force is directly proportional to r⁴.
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Explanation:
I hope this will help you thank you mate
