JIPMER2016PhysicsCenter of Mass, Momentum and Collision
Particles of masses m, 2 m, 3 m, , n m are placed on the same line at distances L, 2 L, 3 L, , n L from O . The distance of centre of mass from O is
Options
- A(2 n+1) L 4
- BL (2 n+1)
- Cn (n^2+1 ) L 2
- D(2 n+1) L 3
Correct answer
D. (2 n+1) L 3
Step-by-step solution
x_ C M = mL+2 m 2 L+ +n m n L m+2 m+ +n m aligned & = L (1^2+2^2+ +n^2 ) (1+2+ +n) & =L n^2 n =L n(n+1)(2 n+1) 6 n(n+1) 2 & = (2 n+1) L 3 aligned