Work done in a Gravitational Feild of a Hemisphere

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SUMMARY

The discussion focuses on calculating the work done by the gravitational field force on a mass 'm' positioned at the center of the base of a hemisphere with mass 'M' and radius 'R'. The user initially calculated the work done as 8GMm/3R based on the potential energy formula, PE = -8GMm/3R. However, the correct answer, as indicated by the reference book, is -3GMm/2R. The discrepancy arises from the user's application of a formula intended for a full sphere, which is not applicable to a hemisphere.

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  • Basic concepts of hemispherical geometry
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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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