Question

A uniform metal sphere of radius a and mass M is surrounded by a thin uniform spherical shell of equal mass and radius 4a (figure 11−E2). The centre of the shell falls on the surface of the inner sphere. Find the gravitational field at the points P1 and P2 shown in the figure
Figure

Answer 1

Explanation:

• It is given that the radius of the uniform metal sphere is a and it’s mass is M.  
• This sphere is surrounded by a thin uniform spherical shell of equal mass and radius 4a.  Also, the centre of the shell falls on the surface of the inner sphere.  
• The gravitational field at the point P1 due to the sphere:

       $M=\frac{C M}{(3 a+a)^{2}}=\frac{C M}{16 a^{2}}$.

• The gravitational field at the point P2 due to the sphere and the shell:

      $M=\frac{G M}{(a+4 a+a)^{2}}+\frac{C M}{(4 a+a)^{2}}=\frac{\left(\frac{61}{900}\right) C M}{a^{2}}$.