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2.Motion in Straight Line
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A bead is free to slide down a smooth wire tightly stretched between points $A$ and $B$ on a vertical circle. If the bead starts from rest at $A$, the highest point on the circle

A
its velocity $v$ on arriving at $B$ is proportional to $cos \theta$
B
time to arrive at $B$ is independent of $\theta$
C
time to arrive at $B$ is proportional to $cos \theta$
D
Both $(A)$ and $(B)$
Solution
$A B=2 R \cos \theta$
$v^{2}=u 6(2)=2 a s$ $v^{2}=2 g \cos \theta \times 2 R \cos \theta$
$v=2 \sqrt{R g} \cos \theta$
$v \propto \cos \theta$
$S=u t+\frac{1}{2} a t^{2}$
$2 R \cos \theta=g \cos \theta t^{2}$
$t=\sqrt{\frac{4 R}{g}} \Rightarrow t=2 \sqrt{\frac{R}{g}}$
Standard 11
Physics