What is analogous to mass in linear motion for rotational motion?

  • A
    Moment of inertia
  • B
    Torque
  • C
    Angular momentum
  • D
    Angular velocity

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Three particles of mass $m$ each are placed at the three vertices of an equilateral triangle. The length of each side of the triangle is $a$. The moment of inertia of this system about any side of the triangle is:

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Match the following columns ($R=$ radius,$k=$ radius of gyration):
Column $I$Column $II$
$(A)$ 'k' for a solid sphere rotating about its tangent$(P)$ $\sqrt{2}R$
$(B)$ 'k' for a ring rotating about its tangent perpendicular to its plane$(Q)$ $\frac{R}{2}$
$(C)$ 'k' for a uniform solid right circular cone rotating about its central axis$(R)$ $\frac{\sqrt{7}}{\sqrt{5}}R$
$(D)$ 'k' for a uniform disc rotating about its diameter$(S)$ $\frac{\sqrt{3}}{\sqrt{10}}R$

Four spheres of diameter $2a$ and mass $M$ are placed with their centers on the four corners of a square of side $b$. The moment of inertia of the system about an axis along one of the sides of the square is

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Four rods are arranged in the form of a square. Calculate the moment of inertia about an axis passing through the center and perpendicular to the plane. (Mass $M$ and length $L$ for each rod)

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$A$ system consists of two identical spheres,each of mass $1.5\, {kg}$ and radius $50\, {cm}$,attached to the ends of a light rod. The distance between the centers of the two spheres is $5\, {m}$. What is the moment of inertia of the system about an axis perpendicular to the rod and passing through its midpoint? (in ${kgm}^{2}$)

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