Question

Consider a semi- circular shell of mass m and radius r which rolls without slipping as shown in Fig. use the fact that maximum kinetic energy at mean position is equal to maximum potential energy at extreme position to find out the frequency of oscillation:

• A. $\omega =\sqrt{\frac{ga(1-cos\theta )}{r(r-a)}}$
• B. $\omega =\sqrt{\frac{g(1-cos\theta )}{(r-a)}}$
• C. $\omega =\sqrt{\frac{ga}{r(r-a)}}$
• D. $\omega =\sqrt{\frac{a(1-cos\theta )}{r(r-a)}}$

Answer 1

The correct option is A $\omega =\sqrt{\frac{ga(1-cos\theta )}{r(r-a)}}$

Kinetic energy at mean position = potential energy at extreme position
$mga(1-cos\theta )=mgr(r-a){\omega }^2$
$\omega =\sqrt{\frac{ga(1-cos\theta )}{r(r-a)}}$