Q.

Three identical spheres, each of mass M, are placed at the comers of a right angle triangle with the 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. [NEET 2020]

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a

2(i^ + j^)

b

(i^ + j^)

c

23(i^ + j^)

d

43(i^ + j^)

answer is C.

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Detailed Solution

The given situation as shown in the figure.                 OA = 2i^                 OB = 2j^Position vector of centre of mass,              RCM=M1r1+M2r2+M3r3M1+M2+M3=M(OA)+M(OB)M+M+M                       =M×2i^+M×2j^3M=23(i^+j^)
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