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:

The adjoining figure shows a force of $40\, N$ acting at $30^o$ to the horizontal on a body of mass $5\, kg$ resting on a smooth horizontal surface. Assuming that the acceleration due to gravity is $10\, ms^{-2}$,which of the following statements is (are) correct?
$[1]$ The horizontal component of the applied force is $20\sqrt{3}\, N$.
$[2]$ The weight of the $5\, kg$ mass acts vertically downwards.
$[3]$ The net vertical force acting on the body is $30\, N$ (upwards).

There are three forces $\vec{F_1}$,$\vec{F_2}$,and $\vec{F_3}$ acting on a body,all acting on a point $P$ on the body. The body is found to move with uniform speed.
$(a)$ Show that the forces are coplanar.
$(b)$ Show that the torque acting on the body about any point due to these three forces is zero.

$A$ 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 $N$):

$A$ body of weight $2 \, kg-wt$ is suspended as shown in the figure. The tension $T_1$ in the horizontal string (in $kg-wt$) is

At the instant $t = 0$,a force $F = kt$ ($k$ is a constant) acts on a small body of mass $m$ resting on a smooth horizontal surface. The force is applied at an angle $\alpha$ with the horizontal. The time at which the body leaves the surface is: