Respuesta :
Answer:
[tex]\dfrac{g_1}{g_2}=0.92[/tex]
Explanation:
It is given that,
The radius of Titan, [tex]r_1=2600\ km=26\times 10^5\ m[/tex]
Density of Titan, [tex]d_1=2.1\ g/cm^3=2100\ kg/m^3[/tex]
Radius of moon, [tex]r_2=1737\ km=1737\times 10^3\ m[/tex]
Density of the moon, [tex]d_2=3.4\ g/cm^3=3400\ kg/m^3[/tex]
Value of gravitational constant, [tex]G=6.67\times 10^{-11}\ m^3kg^{-1}s^{-2}[/tex]
The gravitational acceleration is given by :
[tex]g=\dfrac{GM}{r^2}[/tex]
[tex]g=\dfrac{G\times d\times \pi r^2}{r^2}[/tex]
Let g₁ and g₂ are the gravitational acceleration on Titan and on the moon respectively. So,
[tex]\dfrac{g_1}{g_2}=\dfrac{\dfrac{G\times d_1\times (4/3)\pi r_1^3}{r_1^2}}{\dfrac{G\times d_2\times (4/3)\pi r_2^3}{r_2^2}}[/tex]
[tex]\dfrac{g_1}{g_2}=\dfrac{d_1r_1}{d_2r_2}[/tex]
[tex]\dfrac{g_1}{g_2}=\dfrac{2100\times 26\times 10^5}{3400\times 1737\times 10^3}[/tex]
[tex]\dfrac{g_1}{g_2}=0.92[/tex]
So, the ratio of gravitational acceleration on Titan compared to that on the Moon is 0.92 : 1. Hence, this is the required solution.
