The x, y coordinates of the centre of mass of a uniform L-shaped lamina of mass 3 kg is

Options

A. (5/6 m, 5/6 m)
B. (1 m, 1 m)
C. (6/5 m, 6/5 m)
D. (2 m, 2m)

Answer

A

Explanation

Choosing the x and y axes as shown in the figure.
The coordinates of the vertices of the L-shaped lamina is as shown in the figure. Divide the L-shaped lamina of side 1 m and mass 1 kg (`therefore` the lamina is uniform)

By symmetry, the centres of mass `C_(1), C_(2)` and `C_(3)` of the squares are their geometric centers and have coordinates
`C_(1)(1/2,1/2), C_(2)(3/2,1/2)` and `C_(3)(1/2, 3/2)` respectively.
The coordinates of the center of mass of the L-shaped lamina is:
`X_(CM) = (m_(1)x_(1) + m_(2)x_(2) + m_(3)x_(3))/(m_(1)+m_(2)+m_(3)) = (1 xx 1/2 + 1 xx 3/2 + 1 xx 1/2)/(1 +1+1) = 5/6` m
`Y_(CM) = (m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3))/(m_(1)+m_(2)+m_(3)) = (1 xx 1/2 + 1 xx 1/2 + 1 xx 3/2)/(1+1+1) = 5/6`m