Questions in rotational-motion

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The moment of inertia I of a solid sphere having fixed volume depends upon its volume V as
A thin rod of length L and mass M is bent at the middle point O at an angle of ${{60}^{o}}$ as shown in figure. The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be
The motion of planets in the solar system is an example of the conservation of
A disc is rotating with an angular speed of $\omega$. If a child sits on it, which of the following is conserved
A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about O
Two rigid bodies A and B rotate with rotational kinetic energies $E_A$ and $E_B$ respectively. The moments of inertia of A and B about the axis of rotation are $I_A$ and $I_B$ respectively. If $I_A = I_B /4$ and $E_A = 100 E_B$ the ratio of angular momentum ($L_A$) of A to the angular momentum ($L_B$) of B is
A uniform heavy disc is rotating at constant angular velocity $\omega$ about a vertical axis through its centre and perpendicular to the plane of the disc. Let L be its angular momentum. A lump of plasticine is dropped vertically on the disc and sticks to it. Which will be constant
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 thin circular ring of mass $M$and radius $r$ is rotating about its axis with a constant angular velocity $\omega $. Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity
The earth $E$ moves in an elliptical orbit with the sun $S$ at one of the foci as shown in the figure. Its speed of motion will be maximum at the point

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