Question

A hypothetical planet has a radius 2.7 times that of earth, but has the same mass. what is the acceleration due to gravity near its surface?

Answer 1

Answer:

Acceleration due to gravity at planet will be $1.344m/sec^2$

Explanation:

We have given that radius of the planet = 2.7 × radius of the earth

Mass of the planet = mass of the earth

We know that acceleration due to gravity on the earth is given by

$g=\frac{GM}{R^2}$------EQN 1

Here G is gravitational constant, M is the mass of the earth and R is the radius of the earth

Now acceleration due to gravity on planet

$g_{planet}=\frac{GM}{(2.7R)^2}=\frac{GM}{7.29R^2}$ -----EQN 2

Now after dividing eqn 1 by eqn 2

$\frac{g}{g_{planet}}=\frac{\frac{GM}{R^2}}{\frac{GM}{7.29R^2}}$

$g_{planet}=0.1371g$ = 0.1371×9.8=1.344 $m/sec^2$