Question

An object placed on an equal arm-balance requires $12kg$ to balance it. When placed o a spring scale, the scale reads $12kg$. Everything (balance, scale, set of weights and object) is now transported to the moon where the free fall acceleration is one-sixth to that on the Earth. The new readings of the balance and spring scale (respectively) are:
(A). $12kg,\,12kg$
 (B). $2kg,\,2kg$
(C). $12kg,\,2kg$
(D). $2kg,\,12kg$

Answer 1

Hint: An arm balance is used to measure mass while a spring balance is used to measure the weight. The weight or force of gravity of an object is the product of mass and acceleration due to gravity. While mass is a constant quantity, the weight of the object will vary on the earth and the moon as the acceleration on the moon is one-sixth that of the acceleration on the Earth.
Formulas used:
$W'=\dfrac{W}{6}$

Complete answer:

The above figures show the object when kept on the arm balance and spring balance respectively on earth.
The equal arm balance is used to measure the mass of an object. Therefore, the mass will be constant whether on Earth or on the Moon.
Therefore, the reading of the arm- balance on Earth is $12kg$, reading of arm balance on the Moon is also $12kg$.
The spring scale is used to calculate the weight or the gravitational force of an object. Le the reading of spring balance on the earth be $W$. Therefore,
$W=mg$ - (1)
Given, acceleration due to gravity on the moon is one-sixth the acceleration on the Earth. Therefore,
$W'=m\dfrac{g}{6}$
Here, $W'$ is the weight on an object on the moon.
Therefore, the weight of the object on the moon will be one-sixth the weight on Earth, therefore,
$\begin{align}
  & W'=\dfrac{W}{6} \\
 & \Rightarrow W'=\dfrac{12}{6} \\
 & \therefore W'=2kg \\
\end{align}$
Therefore, the weight of the object on the moon is $2kg$.

The above figure shows the object balanced on arm balance and spring balance respectively on the moon.
Therefore, the reading of the arm balance and the spring balance on the moon are $12kg$, $2kg$ respectively.

Hence, the correct option is (C).

Note:
The arm balance is used to measure the mass of an object using different mass blocks which are used to find the equivalent mass. The spring balance consists of a scale which measured the force on an object. It has a spring constant which is calculated as the force per unit spring extension.