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. $\frac{\sqrt{3m{\omega }^{2}l}}{2}$
• 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 $T_2=0$ .