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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.

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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. ...
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Knowledge Check

  • 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
    B
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    D

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