Question

A hollow sphere rolls down a ${30}^o$ incline of length 6m without slipping. The speed of center of mass a the bottom of plane is

• A. $6m/s^{-1}$
• B. $3m{s}^{-1}$
• C. $6\sqrt{2}m{s}^{-1}$
• D. $3\sqrt{2}m{s}^{-1}$

Answer 1

The correct option is A $6m/s^{-1}$

apply consecration of energy

$E_i=mgh$

$E_i=m10\left(6\sin {30}^{\circ }\right)$

$E_i=30m$

$E_f=\frac{1}{2}m{v}^2+\frac{1}{2}l{\omega }^2$

$E_f=\frac{1}{2}m{R}^2{\omega }^2+\frac{1}{2}\left(\frac{2}{3}m{R}^2\right){\omega }^2$

$E_f=\frac{5}{6}m{R}^2{\omega }^2$

$E_i=E_f$

$R^2{\omega }^2=36$

$v_{cm}=6$