Two planets of radii $r_{1} a n d r_{2}$ are made from the same material having same density. The ratio of acceleration due to gravity $g_{1} {/g}_{2}$ at the surfaces of the planets is

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

r_{1} {/r}_{2}

r_{2} {/r}_{1}

{(r_{1} {/r}_{2})}^{2}

{(r_{2} {/r}_{1})}^{2}

answer is A.

(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

We know,

$g = \frac{G M}{R^{2}}$

$M = ρ X V$ , where $ρ$ is the density and $V$ is the volume.

$g = \frac{G \frac{4}{3} {πR}^{3} ρ}{R^{2}}$

$∴ g = \frac{4}{3} π G ρ R$

$∴ \frac{g_{1}}{g_{2}} = \frac{\frac{4}{3} π G ρ r_{1}}{\frac{4}{3} π G ρ r_{2}} = \frac{r_{1}}{r_{2}}$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE