The coordinates of a triangle ABC are A(2, 4), B(6, 8) and C(–6, –2). Three particles of masses 1 kg, 2 kg and m kg are placed at the vertices of the triangle respectively. If the coordinates of the centre of mass are (2/5,16/5)mass m, in kg will be
Answers
Mass m, in kg will be 2 if The coordinates of a triangle ABC are A(2, 4), B(6, 8) and C(–6, –2) and Three particles of masses 1 kg, 2 kg and m kg are placed at the vertices of the triangle respectively and center of mass are (2/5 , 16/5)
Given : The coordinates of a triangle ABC are A(2, 4), B(6, 8) and C(–6, –2). Three particles of masses 1 kg, 2 kg and m kg are placed at the vertices of the triangle respectively.
The coordinates of the center of mass are (2/5,16/5)
To Find : mass m, in kg
Solution:
For masses m₁ , m₂ and m₃ for vertex (x₁ , y₁) , (x₂ , y₂) and (x₃ , y₃)
center of mass is given by
(m₁x₁ + m₂x₂ + m₃x₃)/(m₁ + m₂ + m₃) , (m₁y₁ + m₂y₂ + m₃y₃)/(m₁ + m₂ + m₃)
Now Vertex are A(2, 4), B(6, 8) and C(–6, –2)
Masses are 1 , 2 and m
Center of mass = (2/5 , 16/5)
2/5 = (1 *2 + 2 * 6 + m (-6))/(1 + 2 + m)
16/5 = (1 *4 + 2 * 8 + m (-2))/(1 + 2 + m)
2/5 = (1 *2 + 2 * 6 + m (-6))/(1 + 2 + m)
=> 2/5 = ( 14 - 6m)/(m + 3)
=> 2m + 6 = 70 - 30m
=> 32m = 64
=> m = 2
or
16/5 = (1 *4 + 2 * 8 + m (-2))/(1 + 2 + m)
=> 16/5 = (20 -2m)/(3 + m)
=> 48 + 16m = 100 - 10m
=> 26m = 52
=> m = 2
mass m, in kg will be 2
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