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

Answer:

T' = 0.9677T

Explanation:

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

$T=2\pi \sqrt{\frac{l}{g}}$

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:

$T'=2\pi \sqrt{\frac{l'}{g}}=2\pi \sqrt{\frac{0.9365l}{g}}=\sqrt{0.9365}(2\pi \sqrt{\frac{l}{g}})=0.9677(2\pi \sqrt{\frac{l}{g}})\\\\T'=0.9677T$

hence, the new period is 0.9677T