An equilateral triangle ABC formed from a uniform wire has two sm… - Vidyadip

MCQ

An equilateral triangle $ABC$ formed from a uniform wire has two small identical beads initially located at $A$. The triangle is set rotating about the vertical axis $AO$. Then the beads are released from rest simultaneously and allowed to slide down, one along $AB$ and the other along $AC$ as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down, are

A
Angular velocity and total energy (kinetic and potential)
✓
Total angular momentum and total energy
C
Angular velocity and moment of inertia about the axis of rotation
D
Total angular momentum and moment of inertia about the axis of rotation

✓

Answer

Correct option: B.

Total angular momentum and total energy

b
The $M I$ about the axis of rotation is not rotation is not constant as the perpendicular distance of the bead with the axis of rotation increases. Also since no external torque is acting, therefore,

$\tau_{e x t}=\frac{d L}{d t}$

$\Rightarrow L=\mathrm{constt.}$

$I \omega=\mathrm{constt.}$

since $l$ increases $\omega$ decreases.

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