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13. The variation of density of a cylindrical thick and long rod, is ρ=ρ0x2L2, then position of its centre of mass from x = 0 end is :-
(1) 2L3
(2) L2
(3) L3
(4) 3L4

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Solution

Dear Student,

let take a disc of dx width at distance x from the x=0. let the radius be r of the cylinder .mass of this disc dm=πr2dx×ρ0x2L2CM=0Lxdm0Ldm=0Lπr2dx×ρ0x3L20Lπr2dx×ρ0x2L2=0Lx3dx0Lx2dx=L44L33=3L4option 4regards

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