Statics Questions

In a right angle $△ABC,$ $\angle A=90^{\circ }$ and sides $a,b,c$ are respectively, $5\text{cm},4\text{cm}$ and $3\text{cm}.$ If a force $\vec{F}$ has moments $0,9$ and $16$ in $\text{N cm}$ units respectively about vertices $A,B$ and $C,$ then magnitude of $\vec{F}$ is

Three forces $\vec{P},\vec{Q}$ and $\vec{R}$ acting along $IA,IB$ and $IC,$ where $I$ is the incentre of a $△ABC,$ are in equilibrium. Then $\vec{P}:\vec{Q}:\vec{R}$ is

With two forces acting at a point, the maximum effect is obtained when their resultant is $4\text{N}.$ If they act at right angles, then their resultant is $3\text{N}.$ Then the forces are

A body weighing $13\text{kg}$ is suspended by two strings $5\text{m}$ and $12\text{m}$ long, their other ends being fastened to the extremities of a rod $13\text{m}$ long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are:

The resultant of two forces $P\text{N}$ and $3\text{N}$ is a force of $7\text{N}$. If the direction of $3\text{N}$ force were reversed, the resultant would be $\sqrt{19}\text{N}$. The value of $P$ is:

$ABC$ is a triangle. Forces $P,Q,R$ acting along $IA,IB$ and $IC$ respectively are in equilibrium, where $I$ is the incentre of $△ABC$. Then $P:Q:R$ is:

$A$ and $B$ are two like parallel forces. A couple of moment $H$ lies in the plane of $A$ and $B$ and is combined with them. The resultant of $A$ and $B$ after combining is displaced through a distance:

The resultant $R$ of two forces acting on a particle is at right angles to one of them and its magnitude is one third of the other force. The ratio of larger force to smaller one is: