Question

A cavity of radius $\frac{R}{2}$ is made inside a solid sphere of radius R . The center of the cavity is located at a distance $\frac{r}{2}$ from the center of sphere. The gravitational force on a particle of mass m at a distance $\frac{R}{2}$ from the center of the sphere on the line joining both the centers of sphere and cavity is ( opposite to the center of cavity ) [ here $g=\frac{GM}{R^2}$ where M the mass of the sphere ].

• A. $\frac{mg}{2}$
• B. $\frac{3mg}{8}$
• C. $\frac{mg}{16}$
• D. $\frac{mg}{4}$

Answer 1

Answer: (B)

$\frac{3mg}{8}$

Answer 2

$E_1 = \frac{\rho R }{6\varepsilon_0}, E_e = \frac{- \rho (R / 2)^3}{3 \varepsilon_0 R^2}$ $E_{net} = E_1 + E_e ; \rho = \frac{M}{\frac{4}{3} \pi R^3} ; \varepsilon_0 = \frac{1}{4 \pi G}$