Question

The density of the core ofa planet is $P_1$ and that of the outer shell is $P_2$ the radii of the core and that of the planet are $R$ and $2R$ respectively. The acceleration due to gravity at the surface ofthe planet is same as ata depth $R$. Find the ratio of $\frac{P_1}{P_2}$

• A. $7:3$
• B. $3:7$
• C. $7:4$
• D. $4:7$

Answer 1

The correct option is A $7:3$

Radius of hollow sphere is $\frac{R}{2}$, so mass in this hollow portion would had been, $\frac{M}{8}$.

Now net force on m due to whole sphere $=$ force due to remaining mass $+$ force due to cavity mass.

$\therefore$ Force due to remaining mass=force due to whole sphere-force due to cavity mass

$=\frac{GMm}{d^2}-\frac{GMm}{8{(d-R/2)}^2}$

$=\frac{GMm}{d^2}[1-\frac{1}{8{(1-\frac{R}{2d})}^2}]$