Question

If a planet has a radius 20% greater than that of the Earth but has the same mass as the Earth, what is the acceleration due to gravity at its surface?

Answer 1

6.81 m/s^2

Step-by-step explanation:

Radius of planet, Rp = R + 0.2R = 1.2 R

where, R is the radius of earth

Mass of planet = mass of earth = M

Let g be the acceleration due to gravity and g' be the acceleration due to gravity on planet.

the formula for acceleration due to gravity on earth

`g=(GM)/(R^(2))` .... (1)

the formula for acceleration due to gravity on planet

`g'=(GM)/(1.44R^(2))` .... (2)

Divide equation (2) be equation (1)

g' = g / 1.44

g' = 9.8 / 1.44 = 6.81 m/s^2

Thus, the acceleration due to gravity on surface of planet is 6.81 m/s^2.

Answer 2

`g_2=6.8125 m^2/sec`

Step-by-step explanation:

We know that

Acceleration due to gravity g is given by the formula

`g= (GM)/(r^2)`

G= gravitational constant

M= mass of the Earth

r= radius of the earth

`g_1 = GM/r_1^2`

Let acc. due to gravity after radius is 20% greater be g_2

then

`g_2=GM/r_2^2`

=> g1/g2 = (r_2/r_1)^2 => g2 = 9.81/1.2^2 = 6.8125