Three identical solid spheres moves down three incline planes A, B and C - all of the same dimensions. A is without friction, the friction between B and sphere is sufficient to cause rolling without slipping, the friction between C and sphere causes rolling with slipping. The kinetic energies on A, B and C at the bottom of the inclines are E_A, E_B and E_C

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E_A = E_B = E_C

E_A = E_B > E_C

E_A > E_B > E_C

E_A > E_B = E_C

answer is B.

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Detailed Solution

In the absence of friction; no loss of energy takes place. When static friction acts on the sphere, there is no slipping between the sphere and the surface and no loss of energy occurs. So E_A = E_B = initial potential Energy. On the plane C, the sphere slips and frictional losses take place.

$∴$ E_C $<$ Initial potential energy. Hence, option - (2) is right.

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