Two uniform solid sphere kd radii R and 2R are at rest with their spheres touching .determine the gravitational force of attraction between them .i the density of spheres be (p)
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Given , density of each sphere is ρ
For finding mass of each sphere , we have to find volume of each
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
Hence, force between them, F = 128π²R⁴ρ²/81
For finding mass of each sphere , we have to find volume of each
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
Hence, force between them, F = 128π²R⁴ρ²/81
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