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Two identical masses, each m, are suspended from the two pans of a balance. The two pans hang at slightly different heights, the vertical separation between them being h. Expressing the answer through the mean density rho of the earth, the error in weighing (the apparent difference in the two weights) is:
- (8/3)*pi*G*rho*m*h
- (4/3)*pi*G*rho*m*h
- (1/3)*pi*G*rho*m*h
- pi*G*rho*m*h
Correct answer: (8/3)*pi*G*rho*m*h
Solution
The two masses sit at heights differing by h, so they experience slightly different g. The weighing error is m times the change in g over h, with dg/dr = -2g/R at the surface. Writing g in terms of rho eliminates R.
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