$A$ 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 ........ $^o$

$A$ block of mass $90 \,kg$ is suspended by three strings $A, B$ and $C$ as shown in the figure. Find the tensions in the strings $A, B$ and $C$ respectively. $\left(g=10 \,ms^{-2}, \sin 37^{\circ}=0.6, \cos 37^{\circ}=0.8\right)$

$A$ particle moving with velocity $\overrightarrow{V}$ is acted upon by three forces represented by the vector triangle $PQR$. The velocity of the particle will

The resultant of two forces,one double the other in magnitude,is perpendicular to the smaller of the two forces. The angle between the two forces is ........ $^o$

$A$ uniform sphere of weight $W$ and radius $R = 3\,m$ is held by a string of length $L = 2\,m$ attached to a frictionless wall as shown in the figure. The tension in the string is:

$A$ block of weight $W$ is suspended by a string and pulled by two horizontal forces $\overline{F}_1$ and $\overline{F}_2$ such that the string makes an angle of $45^{\circ}$ with the vertical. If the tension in the string is $60\,N$, find the magnitude of the horizontal forces $\overline{F}_1$ and $\overline{F}_2$ (assuming they are equal) and the weight $W$ of the block.