A rod of length L has non-uniform linear mass density given by ρ (x) = a + b (x/L)², where a and b are constants and 0 ≤ x ≤ L. The value of x for the centre of mass of the rod is at:

Rotational Motion: JEE Main 2020 Physics question

JEE Main 2020 · 9 Jan, Evening shift · Q6198

JEE Main 20209 Jan, Evening shiftPhysicsMediumRotational Motion140× since 2002

A rod of length L has non-uniform linear mass density given by

\rho

(x) =

a + b{\left( {{x \over L}} \right)^2}

, where a and b are constants and 0

\le

\le

L. The value of x for the centre of mass of the rod is at :