Two particles (A) and (B) are connected by a rigid rod ` AB`. The rod slides along perpendicular rails as shown here. The velocity of (A) to the left is ` 10 m//s`.
What is the velocity of (B) ange ` alpha = 30^@`.
.

Options

A. (a) ` 9.8 m//s`
B. (b) ` 10 m//s`
C. ( 5.8 m//s`
D. ( `17 .3 m//s`

Answer

D

Explanation

Let particle (B) move upwards with velocity (v). At an instant. Let ` OA = x ` and ` OB = y, Ab =l `. Then ltbRgt ` X^2 + y^2 = l^@`
Differentating it with time (t) we have
` 2 x (dx0/(dt) + 2 y (dy)/(dt) =0`
`(dy)/(dt)=- x/y (dx)/(dt) =- (dx //dt)/(tan 30^2) =- 10 xx sqrt 3`
` =- 17. 32 m//s`.