A and B are two smooth pegs on the same horizontal line. An inextensible light string carrying a heavy smooth ring (which can freely slide on the string) passes over the pegs as shown in the figure. The free ends of the string are pulled down vertically with speeds u and v respectively. The speed with which the ring goes up at any instant is

Engineering

Physics

Constrained Relation

Question

A and B are two smooth pegs on the same horizontal line. An inextensible light string carrying a heavy smooth ring (which can freely slide on the string) passes over the pegs as shown in the figure.

The free ends of the string are pulled down vertically with speeds u and v respectively. The speed with which the ring goes up at any instant is

A

$\frac{u + v}{2 cosθ}$

B

$\frac{(u + v) cosθ}{2}$

C

(u + v)/cosθ

D

(u + v)cosθ

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$\frac{1}{2} (\frac{u}{cosθ} + \frac{v}{cosθ}) = \frac{u + v}{2 cosθ}$

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