Question

A ball moves over a fixed track as shown in the figure. From `A` to `B` ball rolls without slipping. Surface `BC` is frictionless. `K_(A), K_(B)` and `K_(C)` are kinetix energies of the ball at `A, B` and `C`, respectively. Then
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A. `h_(A) gt h_(C) , K_(B) gt K_(C)`
B. `h_(A) gt h_(C) , K_(C) gt K_(A)`
C. `h_(A) =h_(C), K_(B) = K_(C)`
D. `h_(A) lt h_(C) , K_(B) gt K_(C)`

Answer 1

Correct Answer - A::B
At `A ME = mgh_(A)`…(1)
at `B ME - K_(B) = K_("rotational") (K_(C))`….(2)
at `C ME = mgh_(C), K_(B) gt K_(C)`
`(B) h_(A) gt h_(C), K_(C) gt K_(A)`
On smooth part `BC`, due to zero torque, angular velocity and hence the rotational kinetic energy remains constant. While moving from `B` to translational kinetic energy converts into gravitational potential energy.