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?

Explanation:

We know that

Acceleration due to gravity g is given by the formula

G= gravitational constant

M= mass of the Earth

r= radius of the earth

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

then

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

6.81 m/s^2

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

  .... (1)

the formula for acceleration due to gravity on planet

  .... (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.