An object of mass $5\, kg$ is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of $10\, N$ throughout the motion. The ratio of time of ascent to the time of descent will be equal to $\left[\right.$Use $g =10 \,ms ^{-2}]$

A block of $\sqrt{3}\,kg$ is attached to a string whose other end is attached to the wall. An unknown force $F$ is applied so that the string makes an angle of $30^{\circ}$ with the wall. The tension $T$ is $...........\,N$ :(Given $g =10\,ms ^{-2}$ )

Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface. The tension in the string will be

A mass of $2\, kg$ suspended with thread $AB$ (figure). Thread $CD$ of the same type is attached to the other end of $2\, kg$ mass. if the lower thread is pulled with a jerk, what happens ?

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