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JEE Main202229 Jul 2022Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

Two bodies of mass 1 kg and 3 kg have position vectors i ^ + 2 j ^ + k ^ and - 3 i ^ - 2 j ^ + k ^ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

Options

  1. Ai ^ - 2 j ^ + k ^
  2. B- 3 i ^ - 2 j ^ + k ^
  3. C- 2 i ^ + 2 k ^
  4. D- 2 i ^ - j ^ + 2 k ^

Correct answer

A. i ^ - 2 j ^ + k ^

Step-by-step solution

As we know, centre of mass is given by, r → com = ∑ m i r → i ∑ m i r → com = m ı ^ + 2 ȷ ^ + k ^ + 3 m - 3 ı ^ - 2 ȷ ^ + k ^ m + 3 m r → com = - 8 m ı ^ - 4 m ȷ ^ + 4 m k ^ 4 m = - 2 ı ^ - ȷ ^ + k ^ The magnitude of the position vector of the centre of mass is 2 2 + 1 1 + 1 2 = 6 . It is similar to the magnitude of the option A.

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