If the linear density (mass per unit length) of a rod of

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If the linear density (mass per unit length) of a rod of length 3m is proportional to x, where x is the distance from one end of the rod, the distance of the centre of gravity of the rod from this end is

1. 2.5 m
2. 1 m
3. 1.5 m
4. 2 m

Correct Option: D

Consider an element of length dx at a distance x from end A.
Here, mass per unit length λ of rod
λ ∝ x ⇒ λ = kx
∴ dm = λdx = kx dx

Position of centre of gravity of rod from end A.