MEDIUM
JEE Main
IMPORTANT
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The position vector of the center of mass rcm  of an asymmetric uniform bar of negligible area of cross-section as shown in figure is:

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Important Questions on Rotational Motion

MEDIUM
JEE Main
IMPORTANT
Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:
MEDIUM
JEE Main
IMPORTANT
The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is Ix. Which one of the graphs represents the variation of I(x) with x correctly?
HARD
JEE Main
IMPORTANT
A particle of mass 20 g is released with an initial velocity 5 m s-1 along the curve from the point A, as shown in the figure. The point A is at height h from point B. The particle slides along the frictionless surface. When the particle reaches point B, its angular momentum about O will be: (Take g=10 m s-2)

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HARD
JEE Main
IMPORTANT

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is:
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HARD
JEE Main
IMPORTANT
From a uniform circular disc of radius R and mass 9 M, a small disc of radius R3 is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is:

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MEDIUM
JEE Main
IMPORTANT
A uniform rod AB is suspended from a point X, at a variable distance x from A, as shown. To make the rod horizontal, a mass m is suspended from its end A. A set of (m, x) value is recorded. The appropriate variables that give a straight line, when plotted, are:

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MEDIUM
JEE Main
IMPORTANT
A force of 40 N acts on a point B at the end of an L-shaped object as shown in the figure. The angle θ that will produce the maximum moment of the force about point A is given by:
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EASY
JEE Main
IMPORTANT
A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes will be:
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