Question

Suppose a vertical tunnel is dug along the diameter of the earth, assumed to be a sphere of uniform mass density $\rho$. If a body of mass $m$ is thrown in this tunnel, its acceleration at a distance $y$ from the centre is given by:

• A. $\frac{4\pi }{3}G\rho ym$
• B. $\frac{3}{4}\pi \rho y$
• C. $\frac{4}{3}\pi \rho y$
• D. $\frac{4}{3}\pi G\rho y$

Answer 1

The correct option is D $\frac{4}{3}\pi G\rho y$

$a=E=\left(\frac{GM}{R^3}\right)y$ (as $a=E=\frac{F}{m}$)

$=\frac{G\left(\frac{4}{3}\pi R^3\rho \right)}{R^3}y$

$=\frac{4}{3}\pi G\rho y$