Two planets of radii r 1 and r 2 are made from the same material- The ratio of the acceleration due to gravity g 1- g 2 at the surface of the two planets is-A- r1B- r1-r02C- r2r2-r1D -r2-r12

You visited us 11 times! Enjoying our articles? Unlock Full Access!

Acceleration Due to Gravity

Two planets o...

Question

Two planets of radii $r_{1}$ and $r_{2}$ are made from the same material. The ratio of the acceleration due to gravity $\frac{g_{1}}{g_{2}}$ at the surface of the two planets is:

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A

Since both the planets are made of the same material, the density of both the planets would be the same.
We know, mass of the planet = volume $\times$ density
Let, $ρ$ be the density of the material.
Volume = $\frac{4}{3}$ $π$ $r^{3}$ , where 'r' is the radius of the planet.
We know, $F = m g = \frac{G M m}{r^{2}}$ $\Rightarrow g = \frac{G M}{r^{2}}$ $= \frac{G \frac{4}{3} π r^{3} ρ}{r^{2}}$
Let radius of first planet be $r_{1}$ and acceleration due to gravity be $g_{1}$
$\Rightarrow$ $g_{1} = G \times \frac{\frac{4}{3} π {r_{1}}^{3} ρ}{{r_{1}}^{2}} = \frac{4}{3} π G r_{1} ρ$ and
for the second planet, let the radius be $r_{2}$ and acceleration due to gravity be $g_{2}$
$\Rightarrow$ $g_{2} = G \times \frac{\frac{4}{3} π {r_{2}}^{3} ρ}{{r_{2}}^{2}} = \frac{4}{3} π G r_{2} ρ$
On dividing $g_{1}$ by $g_{2}$ , we get,
$\frac{g_{1}}{g_{2}} = \frac{r_{1}}{r_{2}}$

Suggest Corrections

Similar questions

Two planets of radii $r_{1}$ and $r_{2}$ are made from the same material. The ratio of the acceleration due to gravity $\frac{g_{1}}{g_{2}}$ at the surface of the two planets is

Two planets of radii $r_{1}$ and $r_{2}$ are made from the same material. The ratio of the acceleration due to gravity $\frac{g_{1}}{g_{2}}$ at the surface of the two planets is:

Two planets of radii $r_{1}$ and $r_{2}$ are of the same mass.

The ratio of the acceleration due to gravity $\frac{g_{1}}{g_{2}}$ at the surface of the two planets is:

Q. Two planets of radii

r_{1}

and

r_{2}

are made from the same material.The ratio of the acceleration of gravity

\frac{g_{1}}{g_{2}}

at the surface of the two planets is-

Two planets have the same average density but their radii are $R_{1}$ and $R_{2}$ . If acceleration due to gravity on these planets be $g_{1}$ and $g_{2}$ respectively, then

Join BYJU'S Learning Program

Two planets of radii r1 and r2 ​are made from the same material. The ratio of the acceleration due to gravity g1g2​ at the surface of the two planets is:

Two planets of radii $r_{1}$ and $r_{2}$ are made from the same material. The ratio of the acceleration due to gravity $\frac{g_{1}}{g_{2}}$ at the surface of the two planets is: