Question

***Physics 12 Question***


Two planets A and B have the same mass. However, the gravitational field strength on the surface of the planet A is 1.20 times the gravitational field strength on the surface of planet B. How does the radius of planet A compare with the radius of planet B?


Please explain and show me your work. Thank you.

Answer 1

the gravity of planet A, is:
\[\Large {g_A} = G\frac{{{M_A}}}{{R_A^2}}\]
where the gravity on the Surface of planet B, is:
\[\Large {g_B} = G\frac{{{M_B}}}{{R_B^2}}\]
now, if we divide such equation side by side together, we get:
\[\Large \frac{{{g_A}}}{{{g_B}}} = \frac{{{M_A}}}{{R_A^2}} \cdot \frac{{R_B^2}}{{{M_B}}} = {\left( {\frac{{{R_B}}}{{{R_A}}}} \right)^2}\]
since \(M_A=M_B\)
now, we use the condition \(g_A=1.2\;g_B\), so we get:
\[\Large\frac{6}{5} = {\left( {\frac{{{R_B}}}{{{R_A}}}} \right)^2}\]
so, what can you conclude?