Define the relationship: W = m × g .

According to Newton's second law, F = m × a Hence, the force of attraction by which the earth attracts the object to the centre of the earth is given by, F = m × g , where, ' g ' is the acceleration due to gravity. By the definition, this force of attraction is called weight and denoted by W . Thus, the above equation becomes, W = m × g

Show that the weight of an object on the moon is 1 6 t h of its weight on the earth.

Let the mass of the body be m . The weight of the body on the earth be W e , the mass of the earth be M e and the radius of the earth be R e . According to the universal law of gravitation, the weight of the body on earth is, W e = G M e m R e 2 . . . ( 1 ) Let the weight of the body on the moon be W m , the mass of the moon be M m and the radius of the moon be R m . According to the universal law of gravitation, the weight of the body on the moon is, W m = G M m m R m 2 . . . ( 2 ) Divide equation 2 by 1 , we get W m W e = G M m m R m 2 G M e m R e 2 ⇒ = M m M e × R e R m 2 … ( 3 ) We know the relation, M e ~ 100 M m R e ~ 4 R m Substituting these equations in equation (iii), we get W m W e = M m 100 M m × 4 R m R m 2 W m W e = 1 100 × 16 1 W m W e = 16 100 W m W e ≅ 1 6 W m ≅ 1 6 W e Hence, the weight of the object on the moon is 1 6 times the weight of the same object on the earth.