A thin, uniform square aluminum plate of side length 40 ,cm has a smaller square…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A thin, uniform square aluminum plate of side length 40\,cm has a smaller square section of side length 20\,cm removed. The removed square is cut out so that its sides are parallel to those of the original plate and its center is initially located at the center of the large square. The plate is then suspended from a pin through what was the large square’s geometric center.
(a) Prove that the plate will hang without rotation when the hole is centered, and state the coordinates of the center of mass relative to the original plate’s center.
(b) The cut-out square is reattached so that its center is shifted 5.0\,cm to the right (positive x-direction) of the large square’s center while remaining in the same plane. Treat the reattached square as a region of negative mass. Determine the new x–coordinate of the system’s center of mass.
(c) For the configuration in part (b), calculate the magnitude and direction of the torque about the pin due to the weight of the plate. Express your answer in terms of the gravitational acceleration g and the areal mass density σ of the aluminum.