Question

A sphere of mass M and radius R₂ has a concentric cavity of radius R_{1 as} shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the center of sphere varies as (0 $\le$ r $\le$ ∞)

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

The whole spece can be divided into three regions

(i) 0 $<$ r $<$ $R_1$ F(r) = 0

(ii) $R_1$ $<$ r < $R_2$ F (r) = $\frac{4}{3}$ $\pi$ G $\rho$ m ( 1 - $\frac{{R_1}^3}{r^2}$)

(iii) $R_2$ $<$ r $<$ $\infty$ F (r) = $\frac{4}{3}$ $\pi$ G $\rho$ m $\frac{{R_2}^3-{R_1}^3}{r^2}$

Here, $\rho$ is the density of matrial of the sphere