The resultant of the system in the figure is a force of $8N$ parallel to the given force through $R$. The value of $PR$ equals to 

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 $m$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius $R$. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass $m$, if the string does not slip on the pulley, is

A massless string is wrapped round a disc of mass $M$ and radius $R$. Another end is tied to a mass $m$ which is initially at height $h$ from ground level as shown in the fig. If the mass is released then its velocity while touching the ground level will be

The moment of inertia of a solid flywheel about its axis is $0.1\,kg-m^2$. A tangential force of $2\,kg\,wt$. is applied round the circumference of the flyweel with the help of a string and mass arrangement as shown in the figure. If the radius of the wheel is $0.1\,m,$ find the angular acceleration of the solid fly wheel (in $rad/sec^2$)

An $L-$ shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If $AB = BC$, and the angle made by $AB$ with downward vertical is $\theta$ then