Question

A uniform metal sphere of radius $a$ and mass $M$ is surrounded by a thin uniform spherical shell of equal mass and radius $4a$. The centre of the shell lies on the surface of the inner sphere. Find the gravitational field intensity at point ${\text{P}}_1$ lying on the same vertical line joining the two centers as shown in the figure.

• A. $\frac{GM}{16a^2}$
  
• B. $\frac{GM}{8a^2}$
• C. $\frac{GM}{2a^2}$
• D. $\frac{GM}{4a^2}$

Answer 1

The correct option is A $\frac{GM}{16a^2}$



The net gravitational field on a point inside a spherical shell of mass $M$ is zero, this is because of the symmetric mass distribution .

Thus, the shell of mass $M$ does not cause any field at point ${\text{P}}_1$.i.e., $E_{shell}=0$

So the field on the point ${\text{P}}_1$ will come due to solid sphere of mass $M$ only.

Since, the distance between point ${\text{P}}_1$ and center of solid sphere is $4a$. So, the net field due to the solid sphere at point ${\text{P}}_1$ is

$E_{net}$=$\frac{GM}{(4a{)}^2}=\frac{GM}{16a^2}$

Hence, option (a) is the correct answer.