Question

The mass of moon is about 0.012 times that of the earth and its diameter is about 0.25 times that of earth. The value of G on the moon will be:
(d) About one-fourth of that on the earth
(b) About one-fifth of that on the earth
(c) About one-sixth of that on the earth
a) Same as that on the earth​

Answer 1

Answer:

answer in d) as the earth is more bigger and heavier

Answer 2

Sorry,For making it complicated........

But if you will try you can understand...........

Explanation:

(c) About one-sixth of that on the earth.

Let's take out thr value of g on earth

Let's take -/

Gravitational constant of earth = G

Mass of earth = M

Radius of earth = R

We know that , g = G×M/(R^2)

Hence,Value of g on earth will be ,

= G×M/(R^2)

Let's take out thr value of g on Moon

Let's take -/

Gravitational constant of Moon = G

Mass of moon = M × 0.012

Radius of moon = R × 0.25

We know that , g = G×M/(R^2)

Hence,Value of g on Moon will be ,

= G×{(M × 0.012)/(R × 0.25)^2}

= G×M/(R^2)× 192/1000

= G×M/(R^2)×1/6

Now, Mass of earth ÷ Mass of moon

= {G×M/(R^2)} ÷ {G×M/(R^2)×1/6}

= 1/6

Hence, value of g on moon is 1/6 as of value of g on earth.