Three identical spheres, each of mass M , are placed at the corners of a right angle triangle with mutually perpendicular sides equal to 2 m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass.

Question

Three identical spheres, each of mass M , are placed at the corners of a right angle triangle with mutually perpendicular sides equal to 2 m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass., 2 i ^ + j ^, i ^ + j ^, 2 3 i ^ + j ^, 4 3 i ^ + j ^

MARKS App · Accepted Answer

First, recall the formula of the center of mass of n particle system, r c m = m 1 r 1 + m 2 r 2 + m 3 r 3 + . . . + m n r n m 1 + m 2 + m 3 + . . + m n ⇒ x com = M × 0 + M × 2 + M × 0 3 M = 2 3 ⇒ y com = M × 0 + M + 2 + M × 0 3 M = 2 3 So the position vector of center of mass is, 2 3 i ^ + 2 3 j ^ .

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