Question

A non-uniform thin rod of length L is placed along x-axis as such its one of ends is at the origin. The linear mass density of rod is l = l₀x. The distance of centre of mass of rod from the origin is :

• A. $\frac{L}{2}$
• B. $\frac{2L}{3}$
• C. $\frac{L}{4}$
• D. $\frac{L}{5}$

Answer 1

Answer: (B)

$\frac{2L}{3}$

Answer 2

x_cm = $\frac{\int_{0}^{L}{\lambda xdx}}{\int_{0}^{L}{\lambda dx}}$ = $\frac{\lambda_{0}\int_{}^{}{x^{2}dx}}{\lambda_{0}\int_{}^{}{xdx}}$ = $\frac{\lbrack x^{3}/3\rbrack_{0}^{L}}{\lbrack x^{2}/2\rbrack_{0}^{L}}$ = $\frac{2}{3}$L