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MHT CET20255 May 2025Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

Three rods of same mass are placed as shown in figure. The co-ordinates of centre of mass of the system are

Options

  1. A( a 3 , a 3 )
  2. B(a, a 2 )
  3. C(2 a, a 2 )
  4. D( 2 a 3 , a 3 )

Correct answer

D. ( 2 a 3 , a 3 )

Step-by-step solution

The center of mass coordinates for the system of three uniform rods, each of mass M , are determined by locating each rod's center and applying the weighted average formula. The vertical rod from (0,0) to (0,a) has center at (0, a 2 ) . The horizontal rod from (0,0) to (2a,0) has center at (a, 0) . The hypotenuse rod from (0,a) to (2a,0) has center at (a, a 2 ) . With total mass 3M , the system's center of mass coordinates are: X_ CM = M(0) + M(a) + M(a) 3M = 2a 3 Y_ CM = M ( a 2 ) + M(0) + M ( a 2 ) 3M = a 3 The r

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