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JEE Main2008PhysicsCenter of Mass, Momentum and CollisionActual

A thin rod of length ' L ' is lying along the x -axis with its ends at x=0 and x=L . Its linear density (mass/length) varies with x ask ( x L )^n , where n can be zero or any positive number. If the position x_ CM of the centre of mass of the rod is plotted against ' n ', which of the following graphs best approximates the dependence of x_ CM on n ?

Correct answer

0

Step-by-step solution

aligned & x_ c m = d m x d m = d x x d m = k ( x L )^n x d x k ( x L )^n d x = [ k x^ n+2 (n+2) L^n k x^ n+1 (n+1) L^n ]₀^L= [ x(n+1) n+2 ]₀^L & x_ c m = L 2 , 2 L 3 , 3 L 4 , 4 L 5 , 5 L 6 , aligned

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