Work done in a Gravitational Feild of a Hemisphere

AI Thread Summary
The discussion focuses on calculating the work done by gravitational force on a mass 'm' positioned at the center of a hemisphere with mass 'M' and radius 'R'. The initial calculation involved finding the center of mass of the hemisphere and applying the potential energy formula, resulting in a work done of 8GMm/3R. However, the correct answer provided in the book is -3GMm/2R, indicating a discrepancy in the method used. The error is identified as the application of a formula meant for a full sphere rather than a hemisphere. Clarification on the correct approach to solve this problem is sought.
Himanshu
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The problem concerns with the work done by the Gravitational Feild force exerted on a mass 'm' kept on the center of the base of a hemisphere of mass "M" radius "R".

The way I did it was, first I found the Center of Mass of the hemisphere which is 3R/8. Next I used the concept => Work done= -Potential Energy.

PE=-8GMm/3R

So Work done would be= 8GMm/3R

Work done by Gravitational Feild force is -8GMm/3R

But the book says the answer is -3GMm/2R

Where am I wrong . Please Help!
 
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Your first formula only applies to a full sphere.
Your method is wrong.
 

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