Question

What is the effect on the period of a pendulum if you decrease its length by 6.35%? (Answer this question in terms of the initial period T.) T' = 0.87703 Incorrect: Your answer is incorrect. T

Answer 1

T' = 0.9677T

Step-by-step explanation:

The period of a pendulum is given by the following formula:

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

l: length of the pendulum

g: gravitational acceleration

If the length of the pendulum is decreased in 6.35% the length of the pendulum becomes:

`l'=l-0.0635l=0.9365l`

The new period for a length of l' is:

`T'=2\pi \sqrt{(l')/(g)}=2\pi \sqrt{(0.9365l)/(g)}=√(0.9365)(2\pi \sqrt{(l)/(g)})=0.9677(2\pi \sqrt{(l)/(g)})\\\\T'=0.9677T`

hence, the new period is 0.9677T