$A$ body of mass $1 \ kg$ is suspended with the help of two strings making angles as shown in the figure. The magnitudes of tensions $T_1$ and $T_2$,respectively,are (in $N$):

$A$ particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (assuming the particle is initially at rest):
$\vec{F}_1 = 5\hat{i} - 5\hat{j} + 5\hat{k}$
$\vec{F}_2 = 2\hat{i} + 8\hat{j} + 6\hat{k}$
$\vec{F}_3 = -6\hat{i} + 4\hat{j} - 7\hat{k}$
$\vec{F}_4 = -\hat{i} - 3\hat{j} - 2\hat{k}$
Then the particle will move:

An iron sphere weighing $10 \, N$ rests in a $V$-shaped smooth trough whose sides form an angle of $60^o$ as shown in the figure. Then the reaction forces are:

One end of a horizontal uniform beam of weight $W$ and length $L$ is hinged on a vertical wall at point $O$ and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point $Q$,at a height $L$ above the hinge at point $O$. $A$ block of weight $\alpha W$ is attached at the point $P$ of the beam,as shown in the figure. The rope can sustain a maximum tension of $(2 \sqrt{2}) W$. Which of the following statement$(s)$ is(are) correct?

Three concurrent co-planar forces $1 \,N$,$2 \,N$,and $3 \,N$ acting along different directions on a body:

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 .........