Three blocks are placed as shown in the figure. The masses of $A$,$B$,and $C$ are $m_1$,$m_2$,and $m_3$ respectively. The force exerted by block $C$ on block $B$ is .........

$A$ spherical ball of mass $m=5\,kg$ rests between two planes which make angles of $30^{\circ}$ and $45^{\circ}$ respectively with the horizontal. The system is in equilibrium. Find the normal forces exerted on the ball by each of the planes. The planes are smooth.

An object is in equilibrium when four concurrent forces,acting in the same plane,are in the directions shown in the figure. Find the magnitudes of $F_1$ and $F_2$.

Three forces $\vec{P}, \vec{Q},$ and $\vec{R}$ act at a point in a plane. The angles between $\vec{P}$ and $\vec{Q}$,and $\vec{Q}$ and $\vec{R}$ are $150^{\circ}$ and $120^{\circ}$ respectively. What is the ratio of the magnitudes of the forces $\vec{P}, \vec{Q},$ and $\vec{R}$ if the system is in equilibrium?

$A$ $1 \,kg$ mass is suspended from the ceiling by a rope. $A$ horizontal force $F$ is applied at the midpoint of the rope so that the upper part of the rope makes an angle of $45^{\circ}$ with respect to the vertical axis as shown in the figure. The magnitude of $F$ is:

$A$ small child tries to move a large rubber toy placed on the ground. The toy does not move but gets deformed under her pushing force $F$,which is obliquely upward as shown in the figure. Then,