Question

Two equal masses each 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?

• A. $\pi G\rho mh$
• B. $\frac{1}{3}\pi G\rho mh$
• C. $\frac{8}{3}\pi G\rho mh$
• D. $\frac{4}{3}\pi G\rho mh$

Answer 1

The correct option is C $\frac{8}{3}\pi G\rho mh$

Force on pans

$1\Rightarrow M{g}_{h}2\Rightarrow Mg$

$\therefore$Error in measurement

$=mg-m{g}_h=mg-mg(1-\frac{2h}{R})$

$=\frac{2mgh}{R}=\frac{2mh}{R}-\frac{GM}{R^2}=\frac{2mh}{R^3}.G.\rho .v$

$=\frac{2mh}{R^3}.G.\frac{4}{3}\pi R^3\rho =\frac{8}{3}m\rho h\pi G$