Question

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

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

Answer 1

Answer: (D)

Mass of the sphere is given by, $M=\frac{4}{3}\pi y^{3}\rho $ ,
gravitational force, $F=\frac{G \left(\frac{4}{3} \pi y^{3} \rho \right) m}{y^{2}}$
$a=\frac{F}{m}$
$a=\frac{G \left(\frac{4}{3} \pi y^{3} \rho \right) m}{y^{2} m}=\frac{4}{3}\pi G\rho y$ .