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AP EAMCET202021 Sep 2020Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

Four identical spheres each of radius (10 ~cm ) and equal mass (1 ~kg ) each are placed on horizontal surface touching each other, so that their centre are located at the vertices of a square of side (20 ~cm ). What is the distance of their centre of mass from the centre of either sphere?

Options

  1. A(20 2 )
  2. B(30 2 )
  3. C(10 2 )
  4. D(40 2 )

Correct answer

C. (10 2 )

Step-by-step solution

The given situation is shown in the figure, (A B=B C=C D=D A=20 ~cm ) Since, all spheres are identical with mass (1 ~kg ) and radius (10 ~cm ) each, hence according to figure, it is clear that all spheres are symmetrically arranged, hence centre of mass will be at intersection point of diagonals of square (A B C D ). ( aligned & A C= 20^2+20^2 =20 2 ~cm & A O=B O=C O=D O= 20 2 2 =10 2 ~cm aligned )

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