Question

The weight of an object on earth is \[800\,{\text{N}}\]. If it were taken to the moon, it would weigh \[100\,{\text{N}}\]. What is its mass on the moon? (Acceleration due to gravity on earth=\[10\,{\text{m}} \cdot {{\text{s}}^{ - 2}}\])
A. \[80\,{\text{kg}}\]
B. \[60\,{\text{kg}}\]
C. \[8\,{\text{kg}}\]
D. \[10\,{\text{kg}}\]

Answer 1

Hint: Use the equation for weight of an object. This formula gives the relation between weight of the object, mass of the object and acceleration due to gravity. The mass of any object at place is the same. Hence, determine the mass of the object on the earth using this formula which will be the required answer.

Formula used:
The weight \[W\] of an object is given by
\[W = mg\] …… (1)
Here, \[m\] is the mass of the object and \[g\] is acceleration due to gravity.

Complete step by step answer:
We have given that the weight of an object on earth is \[800\,{\text{N}}\] and the weight of the same object on the moon is\[100\,{\text{N}}\].
\[{W_E} = 800\,{\text{N}}\]
\[{W_M} = 100\,{\text{N}}\]
Let us determine the mass of the object on the earth using equation (1).
Rewrite equation (1) for weight of the object on the earth.
\[{W_E} = mg\]
Rearrange the above equation for mass \[m\] of the object.
\[m = \dfrac{{{W_E}}}{g}\]
Substitute \[800\,{\text{N}}\] for \[{W_E}\] and \[10\,{\text{m}} \cdot {{\text{s}}^{ - 2}}\] for \[g\] in the above equation.
\[m = \dfrac{{800\,{\text{N}}}}{{10\,{\text{m}} \cdot {{\text{s}}^{ - 2}}}}\]
\[ \Rightarrow m = 80\,{\text{kg}}\]
Hence, the mass of the object is \[80\,{\text{kg}}\].
The weight of an object at different places is different but the mass of any object at any place in the universe is the same.
Therefore, the mass of the object on the moon is also \[80\,{\text{kg}}\].

So, the correct answer is “Option A”.

Note:
The students should read the question carefully. In the question, we have given the value of acceleration due to gravity as \[10\,{\text{m}} \cdot {{\text{s}}^{ - 2}}\]. So, the students should not use the value \[9.8\,{\text{m}} \cdot {{\text{s}}^{ - 2}}\] of acceleration due to gravity which we use normally. Otherwise, the final mass of the object will be close to 80 kg but not exactly 80 kg.