Three sphere of masses m_,m andm_ are located at the vertices of an equilateral triangle having side of same length. Find the moment of inertia of the system about one of side of triangle.

Three sphere of masses m_,m andm_ are located at the vertices of an eq

1.	Three sphere of masses m_,m andm_ are located at the vertices of an equilateral triangle having side of same length. Find the moment of inertia of the system about one of side of triangle.
Answer» `(3)/(4)ml^(2)` `(4)/(3)ml^(2)` `(3)/(2)ml^(2)` `(2)/(3)ML^(2)` SOLUTION : Suppose equilateral triangle `DELTAABC` has length l and mass m are ARRANGED on each of its vertices. The moment of inertia about an axis passing one of side `bar(BC)` of triangle is I, then `I=mr^(2)`, where r = distance of sphere A from BC From right angle `DeltaAPB` `l^(2)=r^(2)+((l)/(2))^(2)` `therefore r^(2)=l^(2)-(l^(2))/(4)=(3l^(2))/(4)` `therefore I=mxx(3l^(2))/(4)` `=(3)/(4)ml^(2)`