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In the figures shown, spheres are identical and angle of inclination and height of all the three inclined planes are same. The rough part of the surface is shown in bold line. If three spheres are released from rest at the respective tops and $K_{A}, K_{B} and K_{C}$ are respectively the energies at the bottom of the inclined plane, then

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$K_{A} < K_{B}$

$K_{A} = K_{B} < K_{C}$

$K_{A} < K_{B} = K_{C}$

$K_{A} = K_{B} > K_{C}$

answer is D.

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Detailed Solution

In first two cases planes are initially rough, so body set into rolling due to torque applied by
friction. In 3rd case, body slides and looses energy.

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