Question

Je to gravity
3. An imaginary planet has a mass 5 times and radius 3 times that of the earth What
is the acceleration due to gravity on the planet, if the acceleration due to gravity on
earth is 10m/s?​

Answer 1

GIVEN:-

• An imaginary Planet has a mass 5 times and radius 3 times that of the earth.

• The Acceleration due to gravity at the earth is 10m/s.

TO FIND:-

• The acceleration due to Gravity at the imaginary planet.

Now,

As , We know

$\rm{g_e = G\dfrac{M_{e}}{r^2}}$.......1

According to Question

M = 5m

r = 3r

Therefore,

Let the planet be "a".

$\implies\rm{g_a =G\dfrac{M_{a}}{r^2}}$

$\implies\rm{g_{a} = G\dfrac{5M_{a}}{(3r)^2}}$

$\implies\rm{g_{a} = G\dfrac{5M_{a}}{9r^2}}$....2

Dividing eq1 & eq2.

$\implies\rm{\dfrac{g_a}{g_e} = \dfrac{ G\dfrac{5M_{a}}{9r^2}} {G\dfrac{M_{e}}{r^2}}}$

$\implies\rm{g_a = \dfrac{5}{9}\times{g_e}}$

$\implies\rm{ g_a = \dfrac{5}{9}\times{10}}$

$\implies\rm{ g_a = \dfrac{50}{9}}$

$\implies\rm{ g_a = 5.5m/s^{-2}}$.

Hence, The Acceleration due to Gravity on the imaginary planet is 5.5m/s^-2.