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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!