$A$ smooth cylinder of mass $m$ and radius $R$ is resting on two corner edges $A$ and $B$ as shown in the figure. The relation between the normal reactions at the edges $A$ and $B$ is

In the figure,the tension in the diagonal string is $60\,N$. Find the magnitude of the horizontal forces $\overline{F}_1$ and $\overline{F}_2$ that must be applied to hold the system in the position shown. What is the weight of the suspended block?

The following forces start acting on a particle at rest at the origin of the coordinate system simultaneously: ${\vec F_1} = -4\hat i - 5\hat j + 5\hat k$,${\vec F_2} = 5\hat i + 8\hat j + 6\hat k$,${\vec F_3} = -3\hat i + 4\hat j - 7\hat k$,and ${\vec F_4} = 2\hat i - 3\hat j - 2\hat k$. The particle will move:

$A$ $50 \, kg$ homogeneous smooth sphere rests on a $30^{\circ}$ incline $A$ and bears against a smooth vertical wall $B$. Calculate the contact force at $A$. (Take $g = 10 \, m/s^2$)

$A$ box of mass $m$ is in equilibrium under the application of three forces as shown below. If the magnitude of $F_1$ is $10 \ N$, what is the magnitude of $F_3$ (in $N$)?

As shown in the figure,the two sides of a step ladder $BA$ and $CA$ are $1.6 \; m$ long and hinged at $A$. $A$ rope $DE$ of length $0.5 \; m$ is tied halfway up. $A$ weight of $40 \; kg$ is suspended from a point $F$,$1.2 \; m$ from $B$ along the ladder $BA$. Assuming the floor to be frictionless and neglecting the weight of the ladder,find the tension in the rope and the forces exerted by the floor on the ladder. (Take $g = 9.8 \; m/s^2$)