Question

Why is the weight of an object less on the moon than on the earth.
A. Density of the moon is less than the density of the earth
B. moon is a satellite of the earth
C. Moon is far from earth
D. Moon’s gravitational force is less than that of earth

Answer 1

Hint: Weight of an object is nothing but the force with which the earth pulls the body towards itself. We know weight is given by \[W=Mg\], where M is the mass of the body and g is the acceleration due to gravity. Since the value of g varies from place to place so at another planet weight at earth will be different than at the planet.

Complete step by step solution:
At earth the value of g=9.8 \[m/{{s}^{2}}\]
It is well known that the value of g at the moon is one-sixth the value of g at earth. So at moon \[{{g}^{'}}=\dfrac{g}{6}\]
So the weight on earth= Mg
The weight on moon=M\[{{g}^{'}}\]= \[\dfrac{Mg}{6}\]

This clearly shows the value of the weight of a body on the moon is one-sixth the value of weight on earth.
This reduction in weight is due to a change in the gravitational force of the earth and not due to any other effect.

Hence the correct option is (D).

Additional Information: Not only with planets but the value of acceleration due to gravity also varies with height and depth. As we go up from the surface of the earth the value of g changes, similarly if we go towards the core the value of g also changes.

Note: The role of density has nothing to play here. Neither the distance varies but what matters is the value of acceleration due to gravity on that planet/satellite which determines the variation of weight.