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  4. A ballet dancer is rotating about his own vertical axis on smooth horizontal floor with a time period 0.5 sec. The dancer folds himself close to his axis of rotation due to which his radius of gyration decreases by 20%, then his time period is

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Q. A ballet dancer is rotating about his own vertical axis on smooth horizontal floor with a time period 0.5 sec. The dancer folds himself close to his axis of rotation due to which his radius of gyration decreases by 20%, then his time period is

NTA AbhyasNTA Abhyas 2020System of Particles and Rotational Motion

Solution:

$I_{1}\omega _{1}=I_{2}\omega _{2}$
$MK_{1}^{2}\frac{2 \pi }{T_{1}}=MK_{2}^{2}\frac{2 \pi }{T_{2}}$
$\frac{T_{2}}{T_{1}} = \left(\right. \frac{K_{2}}{K_{1}} \left.\right)^{2}$
T2 = 0.64 × 0.5
= 0.32 sec