The Particle Race begins!

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 $$10.73$$.

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