Two identical spheres of gold are in contact with each other. The gravitational attraction between them is

Question

Two identical spheres of gold are in contact with each other. The gravitational attraction between them is (A) directly proportional to the square of the radius (B) directly proportional to the cube of the radius (C) directly proportional to the fourth power of the radius (D) inversely proportional to the square of the radius

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/77a1b1ce1986d68be87b15870fe06ac9-.png" /> The gravitational force of attraction between two identical spheres of radius r is F=(G m1 m2/r2)=(G (4/3) π r3 ρ × (4/3) π r3 ρ/(2 r)2) =(4/9) π2 p2 r4 i.e., F propto r4

Q. Two identical spheres of gold are in contact with each other. The gravitational attraction between them is

directly proportional to the square of the radius

directly proportional to the cube of the radius

directly proportional to the fourth power of the radius

inversely proportional to the square of the radius

The gravitational force of attraction between two identical spheres of radius $r$ is
$F = \frac{G m _{1} m _{2}}{r ^{2}} = \frac{G \frac{4}{3} π r ^{3} ρ \times \frac{4}{3} π r ^{3} ρ}{( 2 r ) ^{2}}$
$= \frac{4}{9} π^{2} p^{2} r^{4}$
i.e., $F \propto r^{4}$

Q. Two identical spheres of gold are in contact with each other. The gravitational attraction between them is

directly proportional to the square of the radius

directly proportional to the cube of the radius

directly proportional to the fourth power of the radius

inversely proportional to the square of the radius

The gravitational force of attraction between two identical spheres of radius r is F=r2Gm1​m2​​=(2r)2G34​πr3ρ×34​πr3ρ​ =94​π2p2r4 i.e., F∝r4

The gravitational force of attraction between two identical spheres of radius $r$ is
$F = \frac{G m _{1} m _{2}}{r ^{2}} = \frac{G \frac{4}{3} π r ^{3} ρ \times \frac{4}{3} π r ^{3} ρ}{( 2 r ) ^{2}}$
$= \frac{4}{9} π^{2} p^{2} r^{4}$
i.e., $F \propto r^{4}$