Answer:
T' = 0.9677T
Explanation:
The period of a pendulum is given by the following formula:
[tex]T=2\pi \sqrt{\frac{l}{g}}[/tex]
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:
[tex]l'=l-0.0635l=0.9365l[/tex]
The new period for a length of l' is:
[tex]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[/tex]
hence, the new period is 0.9677T
