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Conservation of Momentum

A ball moves ...

Question

A ball moves over a fixed track as shown in figure. From $A$ to $B$ , the ball rolls without slipping. Surface $B C$ is frictionless. $K_{A}, K_{B}$ and $K_{C}$ are kinetic energies of the ball at $A$ , $B$ and $C$ respectively. Then choose the correct alternative below-

$(a) h_{A} > h_{C}; K_{B} > K_{C} (b) h_{A} > h_{C}; K_{C} > K_{A} (c) h_{A} = h_{C}; K_{B} = K_{C} (d) h_{A} < h_{C}; K_{B} > K_{C}$

A

a, b

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B

a, c

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C

b, d

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D

N o n e o f t h e s e

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Solution

The correct option is A $a, b$
$T . E_{A} = T . E_{B} = T . E_{C} 0 + m g h_{A} = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2} + m g r = \frac{1}{2} I ω^{2} + m g h_{C} S o K_{B} > K_{C} > K_{A} S o h_{A} > h_{C}$

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