Question

Mass is distributed uniformly over a thin triangular
plate and co-ordinates of two vertices are (1 m, 3 m)
and (2 m, -4 m). The co-ordinates of third vertex, if
centre of mass of plate lies at origin are​

Answer 1

Given : Mass is distributed uniformly over a thin triangular  plate

co-ordinates of two vertices are (1 m, 3 m)  and (2 m, -4 m).

centre of mass of plate lies at origin are

To Find : The co-ordinates of third vertex

Solution:

Mass is distributed uniformly

Hence center of mass will be centroid

centre of mass  is origin ( 0 , 0)

=> Centroid = (0 , 0)

(1 m, 3 m)  and (2 m, -4 m).  

Let say third vertex ( x m , y m )

=> ( 1 + 2 + x )/3 = 0   and  ( 3 - 4 + y ) /3  = 0

=> 3 + x  = 0   and ( -1 + y)  = 0

=> x = - 3   and y = 1

third vertex ( -3 m , 1 m )

The co-ordinates of third vertex, ( -3 m , 1 m )

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