A bead is free to slide down a smooth wire tightly stretched betw… - Vidyadip

MCQ

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 $cos \theta$
✓
Both $(A)$ and $(B)$

✓

Answer

Correct option: D.

Both $(A)$ and $(B)$

d
$A B=2 R \cos \theta$

$v^{2}=u 6(2)=2 a s$ $v^{2}=2 g \cos \theta \times 2 R \cos \theta$

$v=2 \sqrt{R g} \cos \theta$

$v \propto \cos \theta$

$S=u t+\frac{1}{2} a t^{2}$

$2 R \cos \theta=g \cos \theta t^{2}$

$t=\sqrt{\frac{4 R}{g}} \Rightarrow t=2 \sqrt{\frac{R}{g}}$

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