question_answer

Direction: Question based on the following paragraph.

Two rods 1 and 2 are released from rest as shown in figure.

Given:\[{{l}_{1}}=4l,{{m}_{1}}=2m,{{l}_{2}}=2l\]and\[{{m}_{2}}=m.\]There is no friction between the two rods. If \[\alpha \]be the angular acceleration of rod 1 just after the rods are released. Then

What is the horizontal force on rod 1 by hinge A at this instant?

A) \[\left( \frac{32-12\sqrt{3}}{3\sqrt{3}} \right)ml\alpha \]      

B) \[\left( \frac{16-2\sqrt{3}}{\sqrt{3}} \right)ml\alpha \]

C) \[(14+2\sqrt{3})ml\alpha \]    

D) \[\sqrt{3}ml\alpha \]

Correct Answer: A

Solution :

\[N-F=(2m){{a}_{c}}=(2m)(2l)\alpha =ml\alpha \] \[\therefore \]\[F=N-4ml\alpha =\left( \frac{32-12\sqrt{3}}{3\sqrt{3}} \right)=ml\alpha \]