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 an (fixed) axis passing through $A$ and normal to 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. $\frac{\sqrt{3 m \omega ^{2} l}}{2}$
• D. zero

Answer 1

Answer: (D)

$B$ moves in dotted circle of radius $l$ with uniform speed. Massless rod 1 can exert force $T_{1}$ on $B$ only along its length. 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 $B$ . Since tangential acceleration of $B$ is zero.


Hence $T_{2}=0$ .