A particle of mass $m$ is constrained to move on $x$-axis. A force $F$ acts on the particle. $F$ always points toward the position labeled E. For example, when the particle is to the left of $E$, $F$ points to the right. The magnitude of $F$ is constant except at point $E$ where it is zero.
The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position $E$ and released from rest at $t=0$
Velocity-time graph of the particle is

A mass of $10\,kg$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of $45^o$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is ..........  $N$ $(g = 10\,ms^{-2})$ 

A rope of length $5\,m$ is kept on frictionless surface and a force of $5\,N$ is applied to one of its end. Find tension in the rope at $1\,m $ from this end ......... $N$

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

A piece of wire is bent in the shape of a parabola $y=k x^2$ ( $y$-axis vertical) with a bead of mass $m$ on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$-axis with a constant acceleration $\alpha$. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the $y$-axis is