Show that the weight of the body on moon =1/6 of the weight of the body in earth.
Let the mass of a given object be M. It weight on earth i.e. the force with which the earth attracts this mass is given by We=G.Me×mR2We=G.Me×mR2…………1 Where Me is the mass of earth Re is its radius and G is the universal gravitational constant. Its vlue of 6.67×10−11Nm2/kg26.67×10-11Nm2/kg2. When that object is taken on the moon its weight (Wm)(Wm) will be given by Wm=G.Mm×mR2mWm=G.Mm×mRm2 Where MmMm is the mass and RmRm is the radius of the moon Dividing 2 by 1 we get WmWe=MmMe×(ReRm)2WmWe=MmMe×(ReRm)2 Now the mass of the earth is about 100 times the mass of the moon and its radius is 4 times that of the moon. ∴WmWe=1100×(4)2=16100=16∴WmWe=1100×(4)2=16100=16 or Wm=We6Wm=We6 Hence the weight of the object on the moon is about one sixth of its weight on earth. It should be noted that mass of the object on the moon is the same as on the earth.
