Q5 of 28 Page 50

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


As the piece Q is removed and glued to centre, the moment of inertia decreases about z-axis as the

M.I


As the distance of that piece from z-axis is decreased to zero, hence its M.I will decrease. Hence, correct option is b.

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3

A particle of mass m is moving in yz-plane with a uniform velocity v with its trajectory running parallel to +ve y-axis and intersecting z-axis at z = a (Fig. 7.2). The change in its angular momentum about the origin as it bounces elastically from a wall at y = constant is:


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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