- #1

Krushnaraj Pandya

Gold Member

- 697

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**1. The problem**

A ball moves without sliding on a horizontal surface. It ascends a curved track upto height h and returns. Value of h is h1 for sufficient rough curved track to avoid sliding and is h2 for smooth curved track, then how are h1 and h2 related (greater, lesser, equal or multiplied by some integral factor)?

**2. Intuitive answer and attempt at solving mathematically**

My first intuition was that friction would hinder translational motion and therefore h1<h2 but then I wondered if the ball is in puring rolling before, it would continue to do so regardless of the surface and so h1 might be equal to h2. I tried conserving energy but friction is present in one case, and even though the work done by friction will be zero I can't figure out how to find both mathematically.

P.S. the answer given is h1>h2