Question

Show that weight of an object on the moon is 1/6th of its weight on earth. (Given: mass of earth =6.37×10^24 kg, mass of moon =7.36×10^22, radius of earth =6.37×10^6m, radius of moon = 1.74×10^6)

Answer 1

Hey!
Given=mass of moon=7.36×10^22
mass of earth=6.37×10^24
radius of moon=1.74×10^6
g=GMm/Rm^2
g=6.67×10^-11*7.36×10^22/(1.74×10^6)^2
g=1.6ms-2
we can put the value of g=9.8ms-2
so,gm/ge=1.6/9.8=1/6
hope it helps you

Answer 2

Dear Student,

◆ Answer -

W' = W/6.458

● Explanation -

Weight of object on earth is -

W = GMm/R^2

Weight of object on moon is -

W' = GM'm/R'^2

Ratio of weight on earth to that of moon -

W/W' = (GMm/R^2) / (GM'm/R'^2)

W/W' = MR'^2 / M'R^2

W/W' = [6.37×10^24 × (1.74×10^6)^2] / [7.36×10^22 × (6.37×10^6)^2]

W/W' = 6.458

W' = W/6.458

Hence, weight of object on moon is approximately 6 times than that at earth.

Thanks dear. Hope this helps you...