Question

gravitational feild intensity due to solid sphere​

Answer 1

Answer:

Let us consider a uniform sphere of mass M. The center of mass is located at point O. We have to calculate the field due to this spherical shell at a test point P, as shown in the figure below. We denote the distance between O and P as r. Let us consider an elementary spherical shell (shown as a shaded region) with mass dM. The field at P due to this element will be

Gravitational Field due to Solid Sphere

\[ dE=\frac{GdM}{r^2}\]

and the direction of the field will be from P to O. Now we can calculate the field due to the sphere by integrating over all the shells making the whole sphere. Thus

\[ E = \int{dE}=\int{\frac{G dM}{r^2}}=\frac{G}{r^2}\int{dM}\]

\[ E= \frac{GM}{r^2}\]

Or,

\[ \boxed{\Vec{E}= -\frac{GM}{r^2}\hat{r}}\]

Where – sign denotes the direction towards the center of sphere.

For an external test point, solid sphere behaves like a point mass placed at the center of the sphere.

Hope it helps