Answer :
If she stands up, thus raising the center of mass of the trapeze + performer system by 35.0 cm, the new period of the system will be 8.79 s.
Given, T = 8.85 s
ΔL = 35.0 cm = 0.35 m
Here, we will apply the formula of time period of simple harmonic motion of pendulum.
T = 2π [tex]\sqrt{L/g[/tex]
8.85 = 2π [tex]\sqrt{L/9.8}[/tex]
L = 19.46 m
After standing up new length
L' = L - ΔL
L' = 19.46 - 0.35
L' = 19.11 m
So, new time period will be
T' = 2π [tex]\sqrt{L'/g}[/tex]
T' = 2π [tex]\sqrt{19.11/9.8}[/tex]
T' = 2 × 3.14 × 1.3964
T' = 8.76 s
So, The new time period will be 8.76 s.
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