Work done in a Gravitational Feild of a Hemisphere

[Himanshu]

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!

 

[pam]

Your first formula only applies to a full sphere.
Your method is wrong.

 

[Moetasim]

Your calculation for the work done by the gravitational field force is correct. However, the book's answer of -3GMm/2R may be referring to the work done by the force of gravity on the mass m as it moves from the center of the base of the hemisphere to the top of the hemisphere. This would involve using the equation W = mgh, where h is the height from the center of the base to the top of the hemisphere. This would result in a work done of -3GMm/2R, as given in the book. It is important to clarify which specific force is being referred to in the problem and in the book's answer.