Question

3 grooves AB,AC and AD are made in a circular disk lying in a vertical plane 3 particles B,C and D constrained to move along path AB,AC and AD respectively are released from point A.Particle B reaches point B in time tB,particle C reaches point C in time tC and particle D reaches at point D in time tD.Then which of the following statements is incorrect
tB=tC=tD
tB>tC=tD
tC>tB>tD
tD=tB>tC

Answer 1

Answer on Question #36180-Physics-Mechanics-Relativity

3 grooves AB, AC and AD are made in a circular disk lying in a vertical plane 3 particles B,C and D constrained to move along path AB,AC and AD respectively are released from point A. Particle B reaches point B in time tB, particle C reaches point C in time tC and particle D reaches at point D in time tD. Then which of the following statements is incorrect

$$tB=tC=tD$$ $$tB>tC=tD$$ $$tC>tB>tD$$ $$tD=tB>tC$$

Answer: all incorrect except tB=tC=tD.

The time taken would be same.

$$s = \frac{a t^{2}}{2}$$ $$a = g \cos \theta$$ $$s = d \cos \theta$$ $$t = \sqrt{\frac{2s}{a}} = \sqrt{\frac{2d \cos \theta}{g \cos \theta}} = \sqrt{\frac{2d}{g}} = \text{const.}$$

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