Respuesta :
Answer:
K1/K2=4
Step-by-step explanation:
The kinetic energy of a rotating sphere is given by:
[tex]K=\frac{I*\omega^{2} }{2}[/tex]
The moment of inertia of a solid sphere is given by
[tex]I=\frac{2MR^{2} }{5}[/tex]
The initial kinetic energy is therefore
[tex]K_1=\frac{2MR^{2}*\omega^{2} }{10}[/tex]
[tex]K_1=\frac{MR_1^{2}*\omega^{2} }{5}[/tex]
The final kinetic energy is given by
[tex]K_2=\frac{MR_2^{2}*\omega^{2} }{5}[/tex]
Therefore the relation K1/K2 if R2 = 0.5R1
[tex]\frac{K_1}{K_2} =\frac{5M(R_1)^{2}*\omega^{2} }{5*M(0.5R_1)^{2} \omega^{2}}[/tex]
The text says nothing about the final angular velocity just the collapse of the collapse of the radius
[tex]\frac{K_1}{K_2} =\frac{1 }{(0.5)^{2} }=4[/tex]
