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Question

Two beads $$A$$ and $$B$$ move along a semicircular wire frame as shown in the figure. The beads are connected by an inelastic string which always remains tight. At an instant the speed of $$A$$ is $$u$$, $$\displaystyle \angle BAC=45^{\circ}$$ and $$\displaystyle BOC=75^{\circ},$$ where $$O$$ is the center of the semicircular arc. The speed of bead $$B$$ at that instant is:

237830.png


A
2u
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B
u
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C
u22
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D
23u
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Solution

The correct option is A $$\displaystyle \sqrt{2}u$$
As the string always remains tight, it may be considered as a rigid body and their is not relative motion between the points along the length of the string. 
Thus the components of $$v$$ and $$u$$ along the string should remain same
$$ucos45^o=vcos60^o$$
or
$$v=\sqrt 2 u$$

335720_237830_ans.png

Physics

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