Question

A ring rolls without slipping on a horizontal surface. At any instant, its position is as shown in the figure. Then:

• A. section $ABC$ has greater kinetic energy than section $ADC$
• B. section $BC$ has greater kinetic energy than section $CD$
• C. section $BC$ has the same kinetic energy as section $DA$
• D. the sections $AB,BC,CD,DA$ have the same kinetic energy

Answer 1

Answer: (A), (B)

The correct options are
A section $ABC$ has greater kinetic energy than section $ADC$
B section $BC$ has greater kinetic energy than section $CD$

As the sphere rolls without slipping, thus $v_D=0$

$⟹v=Rw$

Hence, $v_A=\sqrt{v^2+(Rw{)}^2}$$=\sqrt{v^2+(v{)}^2}=\sqrt{2}v$

Similarly, $v_C=\sqrt{2}v{v}_B=2v$

As the corresponding particles of section $AB$ and $BC$ have similar velocities, thus they have same kinetic energy.

Similarly, section $AD$ and $CD$ have same K.E but different than that of section $AB$ and $BC$.

$⟹$ sections $AB,BC,CD,$and $AD$ donot have same K.E.

Also, velocities of particles in section $ABC$ are greater than that in section $ADC$, thus the former will have greater K.E than the other.