The density of a non-uniform rod of length 1m is given by ρ(x) = a(1+bx2) where an and b are constants and 0≤x≤1. The centre of mass of the rod will be at

A uniform square plate has a small piece Q of an irregular shape removed and glued to the centre of the plate leaving a hole behind (Fig. 7.3). The moment of inertia about the z-axis is then

In problem 7.5, the CM of the plate is now in the following quadrant of x-y plane,

A Merry-go-round, made of a ring-like platform of radius R and mass M, is revolving with angular speed ω. A person of mass M is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round afterwards is

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