Question

Two equals masses each $m$ and $m$ are hung from a balance whose scale pans differ in vertical height by ${}^{\prime }{h}^{\prime }$. 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

Answer: (C)

$\frac{8}{3}\pi G\rho mh$

we know, $g_h=g[1-\frac{2h}{R}]$
$g-g_h=\frac{2gh}{R}$
$g-g_h=2\times \frac{GM}{R^3}h$
$g-g_h=\frac{2Gh}{R^3}\times \frac{4}{3}\pi R^3\rho$
or, $g-g_h=\frac{8}{3}\pi G\rho h$
or, $mg-m{g}_h=\frac{8}{3}\pi G\rho hm$