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JEE Main202225 Jul 2022Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be x m . The value of x is

Correct answer

0

Step-by-step solution

The diagram represents the locations of the masses as mentioned in the question. For point 1 , r 1 → = 0 i ^ + 0 j ^ for point 2 , r 2 → = 3 i ^ + 0 j ^ and for point 3 , r 3 → = 0 i ^ + 3 j ^ . The formula for centre of mass is r → c o m = m 1 r 1 → + m 2 r 2 → + m 3 r 3 → m 1 + m 2 + m 3 ⇒ r → com = M 0 i ^ + 0 j ^ + M 3 i ^ + M 3 j ^ 3 M ⇒ r → com = i ^ + j ^ r → com = 1 2 + 1 2 = 2 = x ⇒ x = 2

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