Question

If a spring balance having frequency $f$ is taken on moon (having $g' = \dfrac{g}{6}$) it will have a frequency of
A. $6f$
B. $\dfrac{f}{6}$
C. $\sqrt {6f}$
D. $\dfrac{1}{{\sqrt 6 }}$

Answer 1

The spring balance measures the weight whereas the beam balance measures the mass. From the question, we are provided that the acceleration due to gravity on earth is different from the moon. We have to find the frequency. So, we are using the formula of time period taking the length of the string to be the same.

Complete step by step answer:
Time period of the pendulum $T = 2\pi \sqrt {\dfrac{L}{g}}$ where $L$ is the length of the string and $g$ is the acceleration due to gravity.Frequency is inverse of the time period $f = \dfrac{1}{T}$
$f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{g}{L}}$ $\ldots \left( 1 \right)$
According to the question, frequency on the moon is given by $g' = \dfrac{g}{6}$
Time period on the moon be given as $T = 2\pi \sqrt{\dfrac{L}{g/6}}$
Frequency on the moon $f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{g}{{6L}}}$ $\ldots \left( 2 \right)$
Comparing the two marked equations,
We get to know that the frequency on the moon decreases by $\dfrac{1}{{\sqrt 6 }}$.

Hence, the correct option is D.

Note: Mass and weight are different. Mass of the object is the amount of matter contained in it. Whereas weight is the force with which the earth pulls the object due to gravity. The weight on the earth and mass are different as both the earth and moon have different acceleration due to gravity.