A demonstration apparatus on a table in the lab is shown in diagram. It consists of a metal track (shown as a thick solid line in the figure below) along which a perfectly spherical marble which can roll without slipping. In one run, the marble is released from rest at a height h above the table on the left section, rolls down one side and then up the other side without slipping, briefly stopping when it has reached $h_1$. Assuming the table to be horizontal and neglecting air drag as well as any energy loss due to rolling,
A demonstration apparatus on a table in the lab is shown in diagram. It consists of a metal track (shown as a thick solid line in the figure below) along which a perfectly spherical marble which can roll without slipping. In one run, the marble is released from rest at a height h above the table on the left section, rolls down one side and then up the other side without slipping, briefly stopping when it has reached $h_1$. Assuming the table to be horizontal and neglecting air drag as well as any energy loss due to rolling,
- A
$h_1 < h$ always, because the friction that keeps the ball rolling must dissipate energy.
- B
$h_1 = h$, since total mechanical energy is conserved.
- C
$h_1 = h$ only if tilt angles $\phi$ and $\theta$ are equal.
- D
$h_1 = h$ only if tilt angle $\phi$ is larger than $\theta$
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- [JEE MAIN 2022]
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