$A$ mass of $5\, kg$ is suspended by a rope of length $2\, m$ from a ceiling. $A$ force of $50\, N$ in the horizontal direction is applied at the mid-point of the rope. The angle made by the rope with the vertical,in equilibrium is ........ $^o$

$A$ small sphere is hung by a string fixed to a wall as shown in the figure. The sphere is pushed from the wall by a stick. The forces acting on the sphere are as shown. Then,identify the incorrect expression.

Write the condition of equilibrium when three forces act on a particle.

Write the similarities and differences between contact force and field force.

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:

$A$ man of mass $50 \,kg$ carries a bag of weight $40 \,N$ on his shoulder. The force with which the floor pushes up his feet will be ......... $N$.