In the given figure a hinged construction is pictured, it consists of two rods with a length 21 . One of the rod's tip is fixed to an unmoving point A and the other rod's tip C moves with a

Question

In the given figure a hinged construction is pictured, it consists of two rods with a length 21 . One of the rod's tip is fixed to an unmoving point A and the other rod's tip C moves with a constant velocity V along a direction which passes the point A at the distance 1 . The acceleration of the connection point B of the rods during the moment when the distance between the point A and C is $2 l$ , is given by $\frac{V ^{2}}{x l}$ . The value of $x$ is.

TestHub · Accepted Answer

At the given time A , B and C form an equilateral triangle. The velocity vector v makes an angle 3 0 ∘ with BC . The velocity of B is perpendicular to AB , due to rotation of AB . Thus velocity of B is also V due to rigidity condition of BC . Thus the acceleration of B towards A is 2 l V 2 ​ (centripetal). Also the relative velocity between B and C is zero so B has no acceleration towards C . But B has tangential acceleration with respect to C . The projection of this a t ​ along AB is 2 l V 2 ​

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