Question

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 _______ .

Answer 1

T' = T√6

Step-by-step explanation:

The time period (T) is given as:

`T = 2\pi\sqrt{(L)/(g)}`

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

`T = 2\pi\sqrt{(L)/(g/6)}`

or

`T = 2\pi\sqrt{(6L)/(g)}`

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

T' = T√6