Two uniform solid cylinders A and B each of mass 1 kg are connected by a spring of constant `200Nm^(-1)` at their axles and are placed on a fixed wedge as shown in fig.There is no friction between cylinders and wedge. The angle made by the line AB with the horizontal, in equilibirum is

Options

A. `0^(@)`
B. `15^(@)`
C. `30^(@)`
D. None of these

Explanation

In equilibrium, there will not be any friction between the cylinder and the wedge. If `theta` be the required angle
Cylinder `A : mg sin60^(@)=kx cos(60^(@)-theta)(-mg cos30^(@))`
Cylinder `B : mg sin30^(@)=kx cos(30^(@)+theta)=kx sin(60^(@)-theta)`
`:. cot30^(@)=cot(60^(@)-theta)rArrtheta=30^(@)`.