Find minimum height of obstacle so that the sphere can stay in equilibrium. 

A $\sqrt{34}\,m$ long ladder weighing $10\,kg$ leans on a frictionless wall. Its feet rest on the floor $3\,m$ away from the wall as shown in the figure. If $F_{f}$ and $F_{w}$ are the reaction forces of the floor and the wall, then ratio of $F _{ a } / F _{f}$ will be:

(Use $\left.g=10\,m / s ^{2}\right)$

A mass $M= 40\  kg$ is fixed at the very edge of a long plank of mass $80\  kg$ and length $1\ m$ which is pivoted such that it is in equilibrium. How far (approx.) from the pivot should a mass of $100\  kg$ be attached so that the plank starts rotating with an angular acceleration of $1\ rad/s^2$?

A disc of radius $5\, m$ is rotating with angular frequency $10\, rad / sec .$ A block of mass $2\, kg$ to be put on the disc friction coefficient between disc and block is $\mu_{ k }=0.4,$ then find the maximum distance from axis where the block can be placed without sliding (in $cm$)

Two uniform rods of equal length but different masses are rigidly joined to form an $L-$ shaped body, which is then pivoted as shown in figure. If in equilibrium the body is in the shown configuration, ratio $M/m$ will be