Calculate the gravitational field intensity and potential at the centre of the base of a solid hemisphere of mass `m`, radius `R`
Text Solution
AI Generated Solution
To solve the problem of calculating the gravitational field intensity and potential at the center of the base of a solid hemisphere of mass \( m \) and radius \( R \), we can follow these steps:
### Step 1: Understand the Geometry
We have a solid hemisphere with a mass \( m \) and radius \( R \). We need to find the gravitational field intensity \( E \) and the gravitational potential \( V \) at the center of the flat base of the hemisphere.
### Step 2: Consider an Element of the Hemisphere
To find the gravitational field intensity, we consider a small element of thickness \( dr \) at a distance \( r \) from the center of the hemisphere. This element can be visualized as a disk with radius \( r \sin \theta \) and thickness \( r d\theta \).
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