Answer:
1.54 s
Explanation:
Considering that the legs constitute 16% of the total weight of the man then mass, [tex]m= \frac {16}{100}\times 67=10.72 Kg[/tex]
The legs also constitute 48% of his height hence [tex]H=\frac {48}{100}\times 1.83=0.8784 m[/tex]
The moment of inertia of a cylinder rotating about a perpendicular axis at one end is [tex]\frac {ml^{2}}{3}[/tex] hence [tex]I=\frac {10.72\times 0.8784^{2}}{3}=2.757135974Kg.m^{2}[/tex]
We also know that the period is given by [tex]2\pi \sqrt{\frac {I}{mgh}}[/tex]
Here, h=0.5H= 0.5*0.8784=0.4392 m
Taking g as 9.81 kg/m2 then
[tex]T= 2\pi \sqrt{\frac {2.757135974}{10.72\times 9.81\times 0.4392}}\\=1.535132615 s\\\boxed{\approx 1.54 s}[/tex]
