Pendulum clock when taken to moon

utkarshakash

1. The problem statement, all variables and given/known data
A pendulum clock that keeps correct time on the earth is taken to the moon. It will run

a) at correct rate
b)6 times faster
c)√6 times faster
d)√6 times slower

2. Relevant equations

3. The attempt at a solution
[itex]T_{earth} = 2\pi \sqrt{\dfrac{L}{g}} \\
T_{moon} = 2\pi \sqrt{\dfrac{L}{g/6}} [/itex]

Dividing i) by ii)

[itex]\dfrac{T_{earth}}{T_{moon}} = \frac{1}{√6} \\
T_{moon} = √6T_{earth} [/itex]

This implies option c) is correct but my book says it is option d).

lewando

The period is longer so the frequency must be...

sankalpmittal

Use concept ,

T [itex]\alpha[/itex] 1/√g

As √g reduces by √6 on moon , this implies time period on moon will be √6 times that of earth , as you got. You interpreted your answer wrongly. If the time period increases , pendulum will oscillate slower or faster for a given displacement of the bob ?

utkarshakash

Thanks for pointing out my mistake

phinds

Forget the math for a minute and just think about it logically. Would you really expect a pendulum clock when moved to lower gravity to have the pendulum swing FASTER? Really ?