Question

On a surface of a planet of radius R and mass M the acceleration due to gravity is 7m/s?. Consider another planet of radius 2R and mass 0.4M. What would the acceleration due to gravity be on this new planet? Show your calculations.

Answer 1

Answer:

0.7 m/$s^{2}$

Explanation:

From Newton's law of universal gravitation,

F = $\frac{GMm}{r^{2} }$

and from Newton's second law of motion,

F = mg

So that;

mg = $\frac{GMm}{r^{2} }$

⇒ g = $\frac{GM}{r^{2} }$

For the first planet,

7 = $\frac{GM}{R^{2} }$

⇒ G = $\frac{7R^{2} }{M}$ .............. 1

For the second planet,

g = $\frac{0.4GM}{(2R)^{2} }$

   = $\frac{0.4GM}{4R^{2} }$

⇒ G = $\frac{4gR^{2} }{0.4M}$ ............. 2

Equating 1 and 2, we have;

$\frac{7R^{2} }{M}$ = $\frac{4gR^{2} }{0.4M}$

g = $\frac{7R^{2} *0.4M}{4R^{2}M }$

  = $\frac{7*0.4}{4}$

  = $\frac{2.8}{4}$

g = 0.7

Therefore, the acceleration due to gravity on the new planet is 0.7 m/$s^{2}$.