Three particles each of mass 5 g are placed at the vertices of an equilateral triangle of side
60 cm. Find:
(i) Distance of its centre of mass from any of its vertex
(ii) Moment of inertia of the system of particles about an axis passing through the centre of
mass of the system and perpendicular to the plane containing them.
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(i) The center of mass of the system is at the centroid of the equilateral triangle formed by the three particles.
The distance of the centroid from any one of the vertex = (length of side of triangle)/√3.
In the given scenario it is 60/√3 cm = 34.641 cm
(ii) The moment of inertia of each body about an axis through the center of mass is MD², where M = mass of each body, D = distance of body from center of mass
Moment of Inertia = 3 x (5g) x (34.641cm)² = 17999.98 g.cm²
The distance of the centroid from any one of the vertex = (length of side of triangle)/√3.
In the given scenario it is 60/√3 cm = 34.641 cm
(ii) The moment of inertia of each body about an axis through the center of mass is MD², where M = mass of each body, D = distance of body from center of mass
Moment of Inertia = 3 x (5g) x (34.641cm)² = 17999.98 g.cm²
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