A particle slides from rest from the topmost point of a vertical circle of radius r along a smooth chord making an angle θ with the vertical. The time of descent is
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a
Least for θ=0
b
Maximum for θ=0
c
Least for θ=45o
d
Independent of θ
answer is D.
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Detailed Solution
a=gsina=gsin90∘−θ=gcosθ l=2RcosθNow using s=ut+12at2, we getl=0t+12gcosθt2⇒ 2Rcosθ=12gcosθt2⇒t=2RgThis is independent of θ.