The Particle Race begins!

Classical Mechanics Level 5

Find the difference in time taken for particles \(P\) and \(Q\) of equal mass and dimensions, to reach point \(B\) of a hemispherical bowl, when \(Q\) is flicked across the diameter \(AB\) through a string and \(P\) slides-down the friction-less surface at \(t=0\), with the same horizontal component of velocity \( v \).

Details and Assumptions:

  • Both the particles are moving from point \(A\) at \(t=0\).

  • Particle \(P\) never leaves the contact off the surface of the bowl.

  • Particle \(Q\) moves along the the string (neglect friction) with a uniform velocity.

  • \(R_{\text{hemisphere}}= 20 \text { m}\), \(m=2 \text { kg}\), \(v=5 \text{ m/s}\), \(g=10 \text{ m/s}^{2}\)

  • If you think \(Q\) reaches first, add \(5.31\) to your difference, otherwise add \(10.73\).

This question is part of the set Best of Me
Title Credits: Simran Malik

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