Question

Two solid spheres of same radius (R) and of same material are placed in such a way that their centres are 2R apart. The gravitational force between them is directly proportional to

Answer 1

Two solid spheres of same radius R and of same material are placed in such a way that their centres are 2R apart.

we know, mass = volume × density

so, mass of each sphere = volume of sphere × density of sphere,

as solid sphere are made of same material so, density will be same . Let us consider density of sphere is $\rho$

so, mass of each sphere, M = 4/3 πR³ × $\rho$

[ as volume of sphere = 4/3 πR³ ]

now, gravitational force between them, F = GM²/(2R)²

= G × {4/3 πR³$\rho$}²/4R²

= G × 16 π²R^6$\rho^2$/36R²

= {4π²$\rho^2$G/9}R⁴

hence, it is clear that gravitational force is directly proportional to R⁴.

Answer 2

Answer:

Two solid spheres of same radius R and of same material are placed in such a way that their centres are 2R apart.

we know, mass = volume × density

so, mass of each sphere = volume of sphere × density of sphere,

as solid sphere are made of same material so, density will be same . Let us consider density of sphere is \rhoρ

so, mass of each sphere, M = 4/3 πR³ × \rhoρ

[ as volume of sphere = 4/3 πR³ ]

now, gravitational force between them, F = GM²/(2R)²

= G × {4/3 πR³\rhoρ }²/4R²

= G × 16 π²R^6\rho^2ρ

2

/36R²

= {4π²\rho^2ρ

2

G/9}R⁴

hence, it is clear that gravitational force is directly proportional to R⁴.