A thick spherical shell has an inner radius R1 and an outer radius R2 . It has mass m and a uniform density. If r is the distance from the centre. Then gravitational field Eg for R1 < r < R2 , is

Q: A thick spherical shell has an inner radius R1 and an outer radius R2 . It has mass m and a uniform density. If r is the distance from the centre. Then gravitational field Eg for R1 < r < R2 , is

(a) $\frac{G m}{\sqrt{2} r^2} [\frac{r^3 – R_1^3}{R_2^3 – R_1^3}]$

(b) $\frac{G m}{2 r^2} [\frac{r^3 – R_1^3}{R_2^3 – R_1^3}]$

(c) $\frac{\sqrt{2} G m}{ r^2} [\frac{r^3 – R_1^3}{R_2^3 – R_1^3}]$

(d) $\frac{G m}{r^2} [\frac{r^3 – R_1^3}{R_2^3 – R_1^3}]$

Ans: (d)