Question

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

• A. $0.1$ sec
• B. $0.25$ sec
• C. $0.32$ sec
• D. $0.4$ sec

Answer 1

The correct option is C $0.32$ sec

Let initial radius of gyration is $R.$

Final radius of gyration $=(R-20)$ of $R=\frac{80}{100}R$

$t_i$ is initial time period

$t_f$ is final time period

According to the law of conservation of angular momentum initial angular momentum$=$ final angular momentum

$or,m\times R^2\times W_i=m\times {\left(\frac{80}{100}R\right)}^2\times W_f$

$0r,{\left(\frac{100}{80}\right)}^2\times \frac{2\pi }{t_i}=\frac{2\pi }{t_f}$

$or,t_f=0.5\times {\left(\frac{4}{5}\right)}^2=0.32\sec$

Hence,

option $\left(C\right)$ is correct answer.