Question

An equilateral triangular frame is made of three thin massless rods. Three point masses of mass $m$ each are fixed at vertices of the frame as shown. The system is rotated with uniform angular speed $\omega $ about a fixed axis passing through $A$ and normal to the plane of triangular frame. Neglect the effect of gravity. The tension in rod connecting mass $B$ and $C$ is

• A. $m\omega ^{2}l$
• B. $\frac{m \omega ^{2} l}{2}$
• C. $\frac{\sqrt{3}}{2}m\omega ^{2}l$
• D. zero

Answer 1

Answer: (D)

$B$ moves in a circle (shown by the dashed curve) of radius $I$ with uniform speed.

Massless rod $1$ can exert force $T_{1}$ on $B$ only along its length i.e. towards the centre of the circular path. Hence $T_{1}$ contributes only to centripetal acceleration of $B$ .
The tension in rod $2$ , that is, $T_{2}$ can contribute to both tangential and centripetal acceleration of $B$ . As the angular speed is uniform so tangential acceleration of $B$ is zero. Hence $T_{2}=0$
The tension in rod connecting mass $B$ and $C$ is zero.