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Q.

P is the centre of mass of a system of four point masses A, B, C and D, which are coplanar but not collineara) P may or may not coincide with one of the point massesb) P must lie within or on the edge of at least one of the triangles formed by taking A, B, C and D three at a timec) P must lie on a line joining two of the points A, B, C, Dd) P lies out side the quadrangle ABCD

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a

a & b are correct

b

c & d are correct

c

a & c are correct

d

b & d are correct

answer is A.

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Detailed Solution

Centre of mass of a two particle system must lie between the particles and on the line joining them . If the cenre of mass of any two particles and other two particles lie on the same striaght line , then only combined centre of mass of A , B , C and D may coincide with one particle.So statement (a) is correct , statement  (b) is also correct .Hence option - (1) is correct.
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P is the centre of mass of a system of four point masses A, B, C and D, which are coplanar but not collineara) P may or may not coincide with one of the point massesb) P must lie within or on the edge of at least one of the triangles formed by taking A, B, C and D three at a timec) P must lie on a line joining two of the points A, B, C, Dd) P lies out side the quadrangle ABCD