Two concentric spherical sheels are as shown in figure. The `V - r` graph will be as

Options

A.
B.
C.
D.

Answer

C

Explanation

for `r le r_(1) V = (Gm_(1))/(r_(1)) - (Gm_(2))/(r_(2)) =` constant
for `r_(1) le r le r_(2) V = - (Gm_(2))/(r_(2)) - (Gm_(1))/(r_(1))`
slope of `V - x` graph `dV//dr = Gm_(1)//r^(2)`
for `r ge r_(2) V = -(G)/(r )(m_(1) + m_(2))`
slope of `V - r "graph" = (G)/(r )(m_(1) + m_(2))`
At the boundary of outer shell slope of `V - r` graph changes form
`(Gm_(1))/(r_(2)^(2))` to `(G(m_(1) + m_(2)))/(r_(2)^(2))` i.e slope increases