A straight rod of length $L$ is made of a material having mass per unit length $m(x)=\lambda|x|$, where $x$ is measured from the centre of rod. The moment of inertia about an axis perpendicular to the rod and passing through one end of the rod will be $L=1 \mathrm{~m}$ and $\lambda=16 \mathrm{~kg} / \mathrm{m}^2$.

Consider a uniform horizontal solid cylinder of mass 10 kg such that its length is 9 times its radius. Let the radius be 40 cm . Calculate the moment of inertia of the cylinder about a line passing through its edge and perpendicular to its axis.

Consider a thin metal strip of mass l kg and length 5 m . Calculate its moment of inertia about an axis perpendicular to strip and located at 100 cm on strip from one its end. (Assume the breadth as the strip is negligible)

A solid cylinder is released from rest from the top of an inclined plane of inclination $30^{\circ}$ and length 60 cm . If the cylinder rolls without slipping, then the speed when it reaches the bottom is