Question

Radius of planet A is twice that of planet B and the density of A is one-third that of B. The ratio of the acceleration due to gravity at the surface of A to that at the surface of B is?
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Answer 1

Answer:The ratio of the acceleration due to gravity is 2:3

Explanation:

Given that,

Radius of planet A is twice that of planet B and the density of A is one-third that of B.

so, the radius is

$r_{A} = 2r_{B}$

The density is

$\rho_{A} = \dfrac{1}{3}\rho_{B}$

We know that,

The acceleration due to gravity

$g = \dfrac{GM}{r^{2}}$

The ratio of the acceleration due to gravity at the surface of A to that at the surface of B is

$\dfrac{g_{A}}{g_{B}} = \dfrac{GM_{A}\times r_{B}^{2}}{GM_{B}\times r_{A}^{2}}$

We know,

Mass = density X Volume

$\dfrac{g_{A}}{g_{B}} = \dfrac{\rho_{A} V_{A}r_{B}^{2}}{\rho_{B} V_{B}r_{A}^{2}}$

$\dfrac{g_{A}}{g_{B}} = \dfrac{\rho_{B} \pi\times r_{A}^{3}_{A}r_{B}^{2}}{3\rho_{B} \pi \times r_{B}^{3}r_{A}^{2}}$

$\dfrac{g_{A}}{g_{B}} = \dfrac{r_{A}}{3r_{B}}$

$\dfrac{g_{A}}{g_{B}} = \dfrac{2 r_{B}}{3r_{B}}$

$\dfrac{g_{A}}{g_{B}} = \dfrac{2}{3}$

Hence, the ratio of the acceleration due to gravity is 2:3.

Answer 2

Answer:

Radius of planet A is twice that of planet B and the density of A is one-third that of B.

so, the radius is

The density is

We know that,

The acceleration due to gravity

The ratio of the acceleration due to gravity at the surface of A to that at the surface of B is

We know,

Mass = density X Volume

Hence, the ratio of the acceleration due to gravity is 2:3.