Question

if a planet has a mass and radius 1/3 of those of earth. calculate the acceleration due to gravity of the planet and compare it with acceleration for to gravity on Earth. if an object has 5kg mass on Earth. calculate it's weight on the planet.

Answer 1

Let us consider the mass of planet is M.

The radius of earth is R.

Hence, the gravitational acceleration of the earth is calculated as -

                                 $g=G\frac{M}{R^2}$

Here, G is the universal gravitational force constant.

The value of $g\ =\ 9.8\ m/s^2$ .

As per the question, the mass of other planet M' = $\frac{1}{3}M$

                                 The radius of the planet R' =  $\frac{1}{3}R$

Hence, the acceleration due to gravity on this planet will be -

                                         $g'=G\frac{M/3}{(R/3)^2}$

                                               $=G\frac{M}{3}\times \frac{9}{R^2}$

                                               $=\ 3G\frac{M}{R^2}$    [2]

From above, we see that the acceleration due to gravity on this planet is three times the acceleration due to gravity on earth.

Hence, g ' = 3g.

Again we are asked to calculate the weight of a 5 kg object on this planet.

The mass of a body is always constant for non relativistic motion. So, the mass of the object on this planet will be the same i.e 5 kg.

The weight of a body is equal to the product of mass with aceleration due to gravity.

Hence, the weight of the object on this new planet will be-

                                    W = mg'

                                         = 5×3g N.

                                         = 5×3×9.8 N

                                         = 147 N.                    [ ans]

                               

Answer 2

Answer:

g'=3g

=> mass remains same

=> weight of the object on the new planet= 147N

(PLEASE CHECK THE ATTACHED IMAGE FOR STEP BT STEP EXPLANATION )

HOPE THIS HELPS!!