The period of a simple pendulum is measured to be t on the earth. if the same pendulum were set in motion on the moon, would its period be .

T' = T√6

Explanation:

The time period (T) is given as:

where,

L is the length of the string of the pendulum

and g is the acceleration due to the gravity on earth

Now on moon, the values of acceleration due to gravity on the moon (g') reduces to one-sixth of the acceleration due to gravity on the earth

Thus,

g' = g/6

substituting the values in the formula for the time period, we get

or

hence, the time period on moon will be √6 times the time period on the earth.

T' = T√6

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