NEETPhysicsCenter of Mass, Momentum and Collision
Four point masses are placed at four corners of a square of side 4 m as shown in the figure. Match the following columns. ( array l|l|l|l & Column I & & Column II (A) & array l x -coordinate of centre of mass of 4 ~kg and 2 ~kg array & (p) & (7 / 2) m (B) & array l x -coordinate of centre of mass of 4 ~kg , 2 ~kg and 3 ~kg array & (q) & 4 / 3 ~m (C) & array l y -coordinate of centre of mass of 1 ~kg , 4 ~kg and 3 ~kg
Options
- A(A-q, B-s, C-p, D-r )
- B(A-p, B-q, C-s, D-r )
- C(A-r, B-s, C-q, D-p )
- D(A-s, B-q, C-r, D-p )
Correct answer
A. (A-q, B-s, C-p, D-r )
Step-by-step solution
Formulas: - x-coordinate of COM: (x= (m i x i) / (m i) ) - (y )-coordinate of COM: ( y = (m i yi ) / (m i ) ) Corner coordinates used above. A. x-coordinate of COM of 4 kg and 2 kg : - Masses at ((0,4) ) and ((4,0) x⁻=(4 0+2 4) /(4+2)=8 / 6=4 / 3 ~m ). B. x-coordinate of COM of (4 ~kg , 2 ~kg ), and 3 kg : - Positions: ((0,4),(4,0),(4,4) ) - (x⁻=(4 0+2 4+3 4) /(4+2+3)=(0+8+12) / 9=20 / 9 ~m ). C. y -coordinate of COM of (1 ~kg , 4 ~kg ), and 3 kg : - Positions: ((0,0),(0,4),(4,4) ) - (y=(1.0+4.4+3.4) /(1+4+3)=(0+16