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

Q. 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

Q. A very long uniform helix is made of thin metal wire. The axis of helix is vertical. A small bead begins to slide down the fixed helix starting from rest. Considering friction between bead and wire of helix to be non-zero, which of the following statements is/ are true as long as bead moves on helix.

Q. Consider an insulated wire frame ABC as shown in a vertical plane. The two beads P and Q are of mass m each and carry charge $q_1$ and $q_2$ respectively and can slide down without any friction along the wires. If they are connected by a wire and are stationary,

Q. Two identical beads, each of m = 100g, are connected by an inextensible massless string, which can slide along the two arms AC and BC of a rigid smooth wire frame in v vertical plane. If the system is released from rest, the kinetic energy of the first bead when the second bead has moved down by a distance of 0.1 m is $x\times {10}^{-3}$ J. Find the value of x (g = 10 $m{s}^{-2}$) (shown situation is after movement of 0.1m).

Q. A smooth uniform rod of length $L$ and mass $M$ has two identical beads of negligible size, each of mass $m$, which can slide freely along the rod. Initially, the two beads are at the centre of the rod and the system is rotating with angular velocity ${\omega }_0$ about an axis perpendicular to the rod and passing through the mid-point $C$ of the rod. There are no external forces. When the beads reach the ends of the rod, then angular velocity of the system is