A thin uniform sheet of metal of uniform thickness is cut into the shape bounded by the line x = a and y = ± k x 2 , as shown. Find the coordinates of the centre of mass.
Text Solution
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Sol.
length of the shaded region = 2y = 2kx 2
dm = 2y dx × ρ
dm = 2kx 2 × ρ dx
M = 
= 
X cm = 
X cm = 
By symmetry the y-coordinate of the shown plate is zero.
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