Solution:
The error in force is \(\Delta F = m(g_1 - g_2) \approx m \frac{2g}{R} h\). Since \(g = \frac{4}{3} \pi G \rho R\), we have \(\frac{2g}{R} = \frac{8}{3} \pi G \rho\). Therefore, \(\Delta F = \frac{8}{3} \pi G \rho m h\).
Two equal masses m and m are hung from a balance whose scale pans differ in vertical height by ‘h’. The error in weighing in terms of density of the earth \(\rho\) is :
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