A ball of mass m and radius R is released from rest from height h₁ on left section of the track as shown in figure. The left and right elevated sections of the track are smooth while the horizontal section is rough. The friction between the ball and rough section of the track is sufficient enough to cause pure rolling motion almost in zero time. The height m reached by the ball on right elevated section of track for the first time is

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may be equal or less than h₁

equal to h₁

less than h₁

information insufficient.

answer is B.

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Detailed Solution

As the ball comes to horizontal level on left end, its gravitational potential energy is converted to translational kinetic energy. As the ball acquires pure rolling motion almost instantly, loss of energy is negligibly small. When the ball starts rising on the right section, its rotational kinetic energy does not change but translational kinetic energy is converted into gravitational potential energy mgh₂. Hence, $h_{2} < h_{1}$ .

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