Two planets have radii r1 and r2 and densities d1 and d2 respectively. Then the ratio of acceleration due to gravity on them will be:

Question

Two planets have radii r1 and r2 and densities d1 and d2 respectively. Then the ratio of acceleration due to gravity on them will be: (A)  r1d1:r2d2  (B)  r1d2:r2d1  (C)  r12d1:r22d2  (D)  r1:r2

Tardigrade Admin · Accepted Answer

The relation between density (D) and acceleration due to gravity (g) is d=(3g/4π ReG) ∴ (d1/d2)=(g1/r1)× (r2/g2) ⇒ (g1/g2)=(d1r1/d2r2)

Q. Two planets have radii $r_{1}$ and $r_{2}$ and densities $d_{1}$ and $d_{2}$ respectively. Then the ratio of acceleration due to gravity on them will be:

$r_{1} d_{1} : r_{2} d_{2}$

$r_{1} d_{2} : r_{2} d_{1}$

$r_{1}^{2} d_{1} : r_{2}^{2} d_{2}$

$r_{1} : r_{2}$

$r_{1} / d_{1} : r_{2} d_{2}$

The relation between density (D) and acceleration due to gravity (g) is
$d = \frac{3 g}{4 π R _{e} G}$
$∴$ $\frac{d _{1}}{d _{2}} = \frac{g _{1}}{r _{1}} \times \frac{r _{2}}{g _{2}}$
$\Rightarrow$ $\frac{g _{1}}{g _{2}} = \frac{d _{1} r _{1}}{d _{2} r _{2}}$

Q. Two planets have radii r1​ and r2​ and densities d1​ and d2​ respectively. Then the ratio of acceleration due to gravity on them will be:

r1​d1​:r2​d2​

r1​d2​:r2​d1​

r12​d1​:r22​d2​

r1​:r2​

r1​/d1​​:r2​d2​​

The relation between density (D) and acceleration due to gravity (g) is d=4πRe​G3g​ ∴ d2​d1​​=r1​g1​​×g2​r2​​ ⇒ g2​g1​​=d2​r2​d1​r1​​