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

In the system shown in the adjoining figure, the tension $T_2$ is

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 ?

Write different type of common forces.

In the figure, blocks $A$ and $B$ of masses $2m$ and $m$ are connected with a string and system is hanged vertically with the help of a spring. Spring has negligible mass. Find out magnitude of acceleration of masses $2m$ and $m$ just after the instant when the string is cut

Define $SI$ unit of force $N$. Define $CGS$ unit of force dyne.