If ME is the mass of the earth and RE its radius, the ratio of the acceleration due to gravity and the gravitational constant is

Question

If ME is the mass of the earth and RE its radius, the ratio of the acceleration due to gravity and the gravitational constant is (A) (R2E/ME) (B) (ME/R2E) (C) MER2E (D) (ME/RE)

Tardigrade Admin · Accepted Answer

The acceleration due to gravity is the same for both, and they are both circles, so unless they have significantly different rolling friction, they would arrive at the same time.

< b r / > As g = \frac{G M _{E}}{R _{E}^{2}} ∴ \frac{g}{G} = \frac{M _{E}}{R _{E}^{2}} < b r / >

Q. If $M_{E}$ is the mass of the earth and $R_{E}$ its radius, the ratio of the acceleration due to gravity and the gravitational constant is

$\frac{R _{E}^{2}}{M _{E}}$

$\frac{M _{E}}{R _{E}^{2}}$

$M_{E} R_{E}^{2}$

$\frac{M _{E}}{R _{E}}$

The acceleration due to gravity is the same for both, and they are both circles, so unless they have significantly different rolling friction, they would arrive at the same time.
$< b r / > As g = \frac{G M _{E}}{R _{E}^{2}} ∴ \frac{g}{G} = \frac{M _{E}}{R _{E}^{2}} < b r / >$

Q. If ME​ is the mass of the earth and RE​ its radius, the ratio of the acceleration due to gravity and the gravitational constant is

ME​RE2​​

RE2​ME​​

ME​RE2​

RE​ME​​