Question

the position vector centre of mass is



3 rd question

Answer 1

Hey there !

Solution:

OA = OB = 1 meter

Mass of all the three = 1 kg

=> M₁ = M₂ = M₃ = 1 Kg

Since O is the origin, O = ( 0,0 )

A = ( 1,0 )

B = ( 0,1 )

So X ( center of mass ) = X₁ * 1 + X₂ * 2 + X₃ * 3 / M₁ + M₂ + M₃

=> X ( center of mass ) = 1 * 1 + 0 * 2 + 0 * 3 / 1 + 1 + 1

=> X ( center of mass ) = 1 + 0 + 0 / 3 = 1 / 3

=> In terms of vector = 1 i / 3 = i / 3

Y ( center of mass ) = Y₁ * 1 + Y₂ * 2 + Y₃ * 3 / M₁ + M₂ + M₃

=> Y ( center of mass ) = 0 * 1 + 0 * 1 + 1 / 1 + 1 + 1

=> Y ( center of mass ) = 0 + 0 + 1 / 3

=> Y ( center of mass ) = 1 / 3

=> In terms of vector we get, 1 j / 3 = j / 3

So we can write it as x + y = i / 3 + j / 3

=> x + y = ( i + j ) / 3

So option 1 is correct.

Hope my answer helped !