Two partical start together from a point `O` and slide down along straight smooth wire inclined at `30^(@)` and `60^(@)` to the vertical plane and on the same slide of vertical through `O` . The relative acceleration of second with respect to first will be of magnitude

Options

A. `(g)/(2)`
B. `(sqrt3 g)/(2)`
C. `(g)/(sqrt3)`
D. `g`

Answer

A

Explanation

`a_(1) = g sin 30^(@) = g//2`
`a_(1) = g sin 60^(@)`
`= sqrt3 g//2`
`a_(r) =|a_(1) - a_(2)|`
Angle between `a_(1)` and `a_(2)` is `30^(@)`
:. `a_(r) = sqrt (a_(1)^2 + a_(2)^2 - 2a_(1) a_(2) cos 30^(@)) = (g)/(2)`