Home
Class 12
PHYSICS
Find the gravitational potential due to ...

Find the gravitational potential due to a spherical shell of mass `M` and radius `R` at `r lt R` and `r gt R`, where `r` is the distance from the centre of the shell.

Text Solution

AI Generated Solution

To find the gravitational potential due to a spherical shell of mass \( M \) and radius \( R \) at distances \( r < R \) and \( r > R \), we can follow these steps: ### Step 1: Gravitational Potential Inside the Shell (\( r < R \)) 1. **Understanding the Shell Theorem**: According to the shell theorem, the gravitational field inside a uniform spherical shell is zero. This means that if you are located anywhere inside the shell (at a distance \( r \) from the center, where \( r < R \)), the net gravitational force acting on you due to the shell is zero. 2. **Gravitational Potential is Constant**: Since the gravitational field \( E \) is zero inside the shell, the gravitational potential \( V \) must be constant throughout the interior of the shell. ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Which one of the following plots represents the variation of the gravitational field on a particle with distance r due to a thin spherical shell of raduis R ? ( r is measured from the centre of the spherical shell).

A point charge Q is placed inside a conducting spherical shell of inner radius 3R and outer radius 5R at a distance R from the centre of the shell. The electric potential at the centre of the shell will be

The electrostatic potential of a uniformly charged thin spherical shell of charge Q and radius R at a distance r from the centre

Using Gauss' law deduce the expression for the electric field due to a uniformly charged sperical conducting shell of radius R at a point (i) outside and (ii) inside the shell. Plot a graph showing variation of electric field as a function of r gt R and r lt R . (r being the distance from the centre of the shell)

Figure shows a hemispherical shell of mass M and radius R and a concentric shell of mass m and radius 3R/4.

A thin spherical shell of mass M and radius R has a small hole. A particle of mass m released at its mouth. Then

A point charge q is placed at a distance of r from the centre O of an uncharged spherical shell of inner radius R and outer radius 2R.The distance r lt R .The electric potential at the centre of the shell will be

A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance of R fro the centre of the shell. The electric potential at the centre of shell will (potential at infinity is zero).

The electric field at a distance 3R//2 from the centre of a charge conducting spherical shell of radius R is E . The electric field at a distance R//2 from the centre of the sphere is

The electric field at a distance 3R//2 from the centre of a charge conducting spherical shell of radius R is E . The electric field at a distance R//2 from the centre of the sphere is