Question

A uniform sphere of mass M and radius R exerts a force F on a small mass m situated at a distance of 2R from the centre O of the sphere. A spherical portion of diameter R is cut from the sphere as shown in the figure. The force of attraction between the remaining part of the sphere and the mass m will be...​

Answer 1

SOLUTION ☺️

Let F1 be the gravitational force on a mass (m) placed at P, which is exerted by the grey colour mass as shown in figure.

Then we have,

==)F= G×Mm/4R^2

==)F1+ G(M/8)m/(9/4)R^2------------(1)

Where LHS of eq^n (1) is the gravitational force due to the full sphere and 2nd term of RHS is the Gravitational force due to the removal sphere.

Proper mass of each sphere is considered.

By solving For F in equation (1), we get

==) F1= 7/36 G×M m/R2

==) 7/9F

HOPE IT HELPS