Two masses $M_1$ and $M_2$ are accelerated uniformly on a frictionless surface as shown in the figure. The ratio of the tensions $T_1/T_2$ is:

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$,the net force on the particle (directed towards the centre) is ($T$ is the tension in the string).

Two unequal masses are connected on two sides of a light string passing over a light and smooth pulley as shown in the figure. The system is released from rest. The larger mass $(2\, kg)$ is stopped $1\, s$ after the system is set into motion and then released. Find the time elapsed before the string becomes tight again. (Take $g = 10\, m/s^2$)

In the system shown in the figure,there is no friction anywhere. The block $C$ $(2 \, kg)$ moves down by a distance $x_0 = 10 \, cm$ with respect to the wedge $D$ $(4 \, kg)$ when the system is released from rest. The velocity of $A$ $(1 \, kg)$ with respect to $B$ $(1 \, kg)$ will be $(g = 10 \, m/s^2)$ ......... $m/s$.

The tension in the string connected between the two blocks is ......... $N$.

Two blocks $A$ and $B$,each of the same mass,are attached by a thin inextensible string through an ideal pulley. Initially,block $B$ is held in position as shown in the figure. Now,block $B$ is released. Block $A$ will slide to the right and hit the pulley in time $t_A$. Block $B$ will swing and hit the surface in time $t_B$. Assume the surface is frictionless. [Hint: Tension $T$ in the string acting on both blocks is the same in magnitude. Acceleration needed for horizontal motion is provided by $T$.]