Two block `A` and `B`move along a semicircular wire frame as shown in figure. The beads are connected by an inelastic string wich always remains tight . At an instant the speed of `A` is `u,/_BAC = 45^(@) and BOC = 75^(@)`,where `O` is the center of the semicircular are. The speed of bead `B` at that instant is

Options

A. `sqrt 2u`
B. u
C. `(u)/(2 sqrt2)`
D. `sqrt((2)/(3) u)`

Answer

A

Explanation

Distance `AB =` constant

`:.` Component of `nu` along `BA =` component of `u` along `BA`
or `nu cos 60^(@) = u cos 45^(@)`
or `nu = sqrt2 u`