A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of x and y coordinates of center of mass of plate in n/9. The value of n i $s_______.$

Question

A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of x and y coordinates of center of mass of plate in n/9. The value of n i s_______.

G1 Physics · Accepted Answer

Image Treat the U-shaped plate as: large rectangle - removed square Using the source dimensions: Mass of the U-shaped plate = 10 kg Mass of the removed square = 2 kg Equivalent full rectangle mass = 12 kg Let centre of mass of U-shaped plate be: (x, y) For x-coordinate: 10x + 2(1.5) = 12(1.5) Therefore: x = 1.5 For y-coordinate: 10y + 2(1.5) = 12(1) Therefore: y = 0.9 Hence: x/y = 1.5/0.9 = 15/9 Therefore: n = 15