Question

what is the weight of an object on the moon​

Answer 1

Answer:

The weight of an object on moon is 1/6th of the weight of the object in earth.

Answer 2

Solution:-

weight of an object at the moon is 1/6 of the weight at the earth.

Let an object of mass M is kept at the surface of the earth.

let me the mass of earth and re the radius of Earth

then weight of the object at earth will be :

→ We = Mge ......(1)

now we know that,

→ ge = GMe/Re²

Let we take object to the surface of moon,

Let Mm be the mass of moon

Rm be the radius of moon

Weight of object at moon will be :

→ Wm = Mgm ......(2)

Where Wm represents weight of object at moon and gm the acceleration due to moon.

Similarly, gm = GMm/Rm²

Dividing (1) by (2),

We/Wm = Mge/Mgm....(3)

Putting values of ge and gm in (3).

We/Wm = GmMe × Rm²/Re² × GmM

→ We/Wm = Me × Rm²/Mm × Re²....(4)

Now mass of Earth is about hundred times more than moon and its radius is about 4 times greater than the moon. So taking these values in equation (4),

We/Wm = 100 × (1)²/1 × (4)²

→ We/Wm = 100/16

→ We/Wm = 6 (Approx)

→ Wm × 6 = We

→ Wm = We/6 - Required expression.

Hence, weight at moon of object is 1/6th than at earth.