The density of the core of a planet is $p_{1}$ and that of the outer part(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 of the planet is same as at a depth R. Find the ratio of $\frac{ρ_{1}}{ρ_{2}}$

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

2 : 5

5 : 3

7 : 3

1 : 3

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Let $m_{1}$ be the mass of the core and $m_{2}$ be the mass of outer shell $g_{1} = g_{2}$

$\Rightarrow \frac{{Gm}_{1}}{R^{2}} = \frac{G (m_{2} + m_{1})}{4 R^{2}}$

$\Rightarrow 4 m_{1} = m_{1} + m_{2} \Rightarrow 3 m_{1} = m_{2}$

$\Rightarrow 3 [\frac{4}{3} π R^{3} ρ_{1}] = \frac{4}{3} π [8 R^{3} - R^{3}] ρ_{2}$

$\Rightarrow 3 ρ_{1} = 7 ρ_{2} \Rightarrow ρ_{1} : ρ_{2} = 7 : 3$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE