Question

How much does a 78.0 Kg student weight on earth \[(g=9.8m{{s}^{-2}})\]and on moon\[(g=1.60m{{s}^{-2}})\]?

Answer 1

Hint: The weight of the body can be measured by doing the product of its mass and acceleration due to gravity experienced by them. Mass is totally independent of acceleration due to gravity while weight will totally depend on it. The SI unit of mass is Kg and the SI unit of Weight is Newton. Value of acceleration due to gravity is different in different places.

Complete answer:
Here the mass of man is given in the question as 78.0 Kg.
 We have to find the Weight of man on earth and moon.
So for that purpose we should use the relation between weight ,mass and acceleration due to gravity which can be expressed as \[W=mg\].
Where,
W represents Weight of body.
m represents mass of the body.
g represents acceleration due to gravity.
Generally mass is a measure of matter an object contains, and weight is a measure of the force of gravity acting on the object. Weight can only change due to change in the value of acceleration due to gravity. The moon value of acceleration due to gravity is \[\dfrac{g}{6}\]where g is the acceleration due to gravity on earth.
Weight is also defined as a kind of force which acts vertically downwards and always acts towards the centre of earth.
Since acceleration due to gravity on moon is\[(g=1.60m{{s}^{-2}})\]which is already given in the questions otherwise we will use \[\dfrac{g}{6}\]value where g is the acceleration due to gravity of earth.
So the weight of man on moon is expressed as-
\[{{W}_{moon}}={{m}_{man}}{{g}_{moon}}\]
\[{{W}_{moon}}=78\times 1.60\]
\[{{W}_{moon}}=124.8N\]
Since acceleration due to gravity on earth \[(g=9.8m{{s}^{-2}})\]is given in the question.
So the weight of man on earth is expressed as-
\[{{W}_{earth}}={{m}_{man}}{{g}_{earth}}\]
\[{{W}_{earth}}=78\times 9.8\]
\[{{W}_{earth}}=764.4N\]
Hence ,
Weight of body on earth \[=764.4N\]
Weight of body on moon \[=124.8N\]
Mass of the body will never change because it is independent of acceleration due to gravity.
Mass indicates the total matter contained in the body and at every place total matter remains the same.

Note:
Generally we deal with phenomena in our daily life in which weight and mass are regularly used. We always expressed weight in our daily lives in kilograms rather than in Newton. For example Weight of a person is 50 Kg.This statement is wrong because weight is always expressed in Newton. So the correct statement is that the mass of a person is 50 kg.