Two identical solid copper spheres of radius R are placed in contact with each other. The gravitational attraction between them is proportional to:

Question

Two identical solid copper spheres of radius R are placed in contact with each other. The gravitational attraction between them is proportional to: (A)  R2  (B)  R-2  (C)  R4  (D)  R-4

Tardigrade Admin · Accepted Answer

F=(GMM/R2) =(G( (4/3)π R3ρ )( (4/3)π R3ρ )/R2) ∴ F propto R4

Q. Two identical solid copper spheres of radius $R$ are placed in contact with each other. The gravitational attraction between them is proportional to:

$R^{2}$

$R^{- 2}$

$R^{4}$

$R^{- 4}$

$R^{3}$

$F = \frac{GMM}{R ^{2}}$ $= \frac{G ( \frac{4}{3} π R ^{3} ρ ) ( \frac{4}{3} π R ^{3} ρ )}{R ^{2}}$
$∴$ $F \propto R^{4}$

Q. Two identical solid copper spheres of radius R are placed in contact with each other. The gravitational attraction between them is proportional to:

R2

R−2

R4

R−4

R3

F=R2GMM​ =R2G(34​πR3ρ)(34​πR3ρ)​ ∴ F∝R4