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Question: Answered & Verified by Expert
A non-uniform thin rod of length L is placed along the x-axis such that one of its ends is at the origin. The linear mass density of the rod is λ=λ0 x. Find the distance of the centre of mass of the rod from the origin.
PhysicsCenter of Mass Momentum and CollisionNEET
Options:
  • A L2
  • B 2L3
  • C L4
  • D L5
Solution:
1731 Upvotes Verified Answer
The correct answer is: 2L3
The mass of considered element is

dm = λ dx = λ 0  xdx


    


∴      x cm = 0 L xdm dm = 0 L x λ 0 xdx 0 L λ 0 xdx

= λ 0 x 3 3 0 L λ 0 x 2 2 0 L = λ 0 L 3 3 λ 0 L 2 2 = 2 3 L

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