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# Weight of a man measured on earth is $600N$. What would be his weight on the moon?(A) $600N$(B) $100N$(C) $200N$(D) $1200N$

Last updated date: 20th Jun 2024
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Hint We know that acceleration due to gravity on the moon is approximately $(1/6)th$ of acceleration due to gravity on earth because the size and mass of the moon is less in comparison to earth. Weight of an object is dependent on the mass of the object and the acceleration of the object. Then the weight of an object changes with change in acceleration of object or change in acceleration due to gravity.

Complete step by step solution
We know that acceleration due to gravity on the moon is approximately $(1/6)th$ of acceleration due to gravity.
Weight of an object is dependent on the mass of the object and the acceleration of object means weight is equal to product of mass and acceleration due to gravity.
The weight of man on earth is $600N$.
Let $m$ is mass of an object, ${g_{earth}}$ is acceleration due to gravity on earth and ${g_{moon}}$ is acceleration due to gravity on moon.
${g_{moon}} = \dfrac{{{g_{earth}}}}{6}$ -(1)
${W_{earth}} = {g_{earth}} \times m$ or $m = \dfrac{{{W_{earth}}}}{{{g_{earth}}}} = \dfrac{{600}}{{{g_{earth}}}}N$ -(2)
Similarly, ${W_{moon}} = m \times {g_{moon}}$ -(3)
Using (1) and (2) in (3), we get
${W_{moon}} = \dfrac{{600}}{{{g_{earth}}}} \times \dfrac{{{g_{earth}}}}{6} = \dfrac{{600}}{6} = 100N$

Hence the correct answer is option B.

Note Weight of a person is dependent on its acceleration. If a person is at rest on earth and the same person is sitting in an accelerated bus then its weight in these two conditions are not the same weight of the person as when he is at rest.