$A$ 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:

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).

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:

Three forces start acting simultaneously on a particle moving with velocity $\vec{v}.$ These forces are represented in magnitude and direction by the three sides of a triangle $ABC$ (as shown). The particle will now move with velocity

$A$ rope of mass $5 \,kg$ is hanging between two supports as shown. The tension at the lowest point of the rope is close to ........... $N$ (take $g=10 \,m/s^2$).

In the given arrangement,the normal force applied by the block on the ground is