From a sphere of mass M and radius R, a smaller sphere of radius (R/2) is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two spheres is :

Question

From a sphere of mass M and radius R, a smaller sphere of radius (R/2) is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two spheres is : (A) (41 GM2/3600 R2) (B) (41 GM2/450 R2) (C) (59 GM2/450 R2) (D) (GM2/225 R2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/e917699daeb26ec7a8744f59d71b3d70-.png" /> Field at 3R is (GM/9R2) at P Due to cavity field at P is (GM/8(2.5R)2) = (GM/50R2)

$\frac{41 G M ^{2}}{3600 R ^{2}}$

$\frac{41 G M ^{2}}{450 R ^{2}}$

$\frac{59 G M ^{2}}{450 R ^{2}}$

$\frac{G M ^{2}}{225 R ^{2}}$

Field at 3R is $\frac{GM}{9 R ^{2}}$ at P
Due to cavity field at P is $\frac{GM}{8 ( 2.5 R ) ^{2}} = \frac{GM}{50 R ^{2}}$

3600R241GM2​

450R241GM2​

450R259GM2​

225R2GM2​

Field at 3R is 9R2GM​ at P Due to cavity field at P is 8(2.5R)2GM​=50R2GM​

$\frac{41 G M ^{2}}{3600 R ^{2}}$

$\frac{41 G M ^{2}}{450 R ^{2}}$

$\frac{59 G M ^{2}}{450 R ^{2}}$

$\frac{G M ^{2}}{225 R ^{2}}$

Field at 3R is $\frac{GM}{9 R ^{2}}$ at P
Due to cavity field at P is $\frac{GM}{8 ( 2.5 R ) ^{2}} = \frac{GM}{50 R ^{2}}$