Question

The weight of a body is 120 N on the earth. If it is taken to the moon, its weight and mass will be about (Take \[{{g}_{e}}=10\,{m}/{{{s}^{2}}}\;\])
A. 120 N, 120 kg
B. 60 N, 12 kg
C. 20 N, 12 kg
D. 720 N, 120 kg

Answer 1

Hint: The mass of the object/body remains the same throughout the universe. Whereas, the weight of the body changes. The gravitational energy on the moon is less when compared to the gravitational energy on the earth, thus the weight of the body changes, whereas, the mass remains the same.

Formula used:
\[W=mg\]
\[{{W}_{m}}=\dfrac{1}{6}\times {{W}_{e}}\]

Complete answer:
From given, we have,
The weight of a body on the earth is, \[{{W}_{e}}=120\,N\]
The gravitational constant of the earth is, \[{{g}_{e}}=10\,{m}/{{{s}^{2}}}\;\]
The mass of the body on the earth is given by the formula,
\[{{W}_{e}}={{m}_{e}}\times {{g}_{e}}\]
Where \[{{W}_{e}}\]is the weight of the body on the earth, \[{{m}_{e}}\]is the mass of the body on the earth and \[{{g}_{e}}\]is the gravitational constant of the earth.
Substitute the given values in the above equation to find the mass of the body on the earth.
\[\begin{align}
  & {{W}_{e}}={{m}_{e}}\times {{g}_{e}} \\
 & 120={{m}_{e}}\times 10 \\
 & {{m}_{e}}=\dfrac{120}{10} \\
 & {{m}_{e}}=12\,kg \\
\end{align}\]
Therefore, the mass of the body on the earth is 12 kg.
As the mass remains the same throughout the universe, the mass of the body on the moon will be,
\[{{m}_{e}}={{m}_{m}}=12\,kg\]
Therefore, the mass of the body on the earth is 12 kg.
Now we need to find the weight of the body on the moon.
The formula for calculating the weight of the body on the moon is,
\[{{W}_{m}}=\dfrac{1}{6}\times {{W}_{e}}\]
Where \[{{W}_{e}}\]is the weight of the body on the earth and \[{{W}_{m}}\] is the weight of the body on the moon.

Substitute the given values in the above equation to find the weight of the body on the moon.
\[\begin{align}
  & {{W}_{m}}=\dfrac{1}{6}\times {{W}_{e}} \\
 & {{W}_{m}}=\dfrac{1}{6}\times 120 \\
 & {{W}_{m}}=20\,N \\
\end{align}\]

As the weight and mass of the body on the moon is 20 N, 12 kg, option (C) 20 N, 12 kg is correct.

Note:
The things to be on your figure tips for further information on solving these types of problems are:
Only the weight of the body changes when replaced from the earth to the moon, but the mass remains unchanged, because the weight of the body is influenced by the gravitational force. So, in order to confuse the students, along with the weight of the body, the mass of the body will also be asked.