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 [2000]

Question

Smart Achievers · Accepted Answer

(2)

Due to increase in perpendicular distance of the bead with the axis of rotation, $M . I .$ about the axis of rotation is not constant. So $I$ increases.

There is no external torque acting

$∴$ $τ_{ext} = \frac{d L}{d t} \Rightarrow L = constant \Rightarrow I ω = constant$

But, $I$ increases so $ω$ decreases.

Solution

1 angular velocity and total energy (kinetic and potential)

2 total angular momentum and total energy

3 angular velocity and moment of inertia about the axis of rotation

4 total angular momentum and moment of inertia about the axis of rotation

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