A thin bar of length has a mass per unit length

PHYSICS · Single correct · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A thin bar of length

L

has a mass per unit length

\lambda

, that increases linearly with distance from one end. If its total mass is

M

and its mass per unit length at the lighter end is

\lambda_0

, then the distance of the centre of mass from the lighter end is: (1)

\frac{L}{2} - \frac{\lambda_0 L^2}{4M}

(2)

\frac{L}{3} + \frac{\lambda_0 L^2}{8M}

(3)

\frac{L}{3} + \frac{\lambda_0 L^2}{4M}

(4)

\frac{2L}{3} - \frac{\lambda_0 L^2}{6M}