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Masses, assumed to be equal to \( m \) each, hang from strings
\( \mathrm{P} \) of different lengths from the ends of a balance on the surface of the earth. If the strings have negligible mass and differ in length
W by \( h \), show that the crror in weighing, \( W^{\prime}-W \), is given by \( W^{\prime}- \) \( W=\frac{8 \pi}{3} G m \rho h \), where \( \rho \) is the density of the earth.
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