In figure, two identical particles each of mass $m$ are tied together with an inextensible light string. This is pulled at its centre with a constant force $F$. If the whole system lies on a smooth horizontal plane, then the acceleration of approach of particles towards each other at the instant shown in figure is:

A block of mass $m$ lies on wedge of mass $M,$ which lies on fixed horizontal surface. The wedge is free to move on the horizontal surface. A horizontal force of magnitude $F$ is applied on block as shown, neglecting friction at all surfaces, the value of force $F$ such that block has no relative motion w.r.t. wedge will be : (where $\mathrm{g}$ is acceleration due to gravity)

Acceleration (with respect to ground) of pulleys and blocks are as shown in the figure. All pulleys and strings are massless and  frictionless than the magnitude of $a_A$ and $a_B$ are:

A wedge is moving with an acceleration $a=4 \mathrm{m} {\mathrm{s}}^{-2}$ vertically up as shown in figure. What is acceleration of block of mass $1 \mathrm{kg}$ with respect to wedge and normal reaction by wedge on block respectively. All surfaces are smooth. Choose correct pair : $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Two smooth rings $A$ and $B$ are connected by a string. Another string connects Ring  $A$ and block, if strings are tight then at the given moment :

Two blocks of mass $2 \mathrm{kg}$ and $3 \mathrm{kg}$ are placed in a cart. A variable force $F$ is acting on the cart. At an instant acceleration of different blocks and cart are as shown. Find value of $F$ at this instant (mass of cart is $10 \mathrm{kg}$ ) All accelerations are horizontal.

A mass of $1 \mathrm{kg}$ is suspended by a string $A$. Another string $C$ is connected to its lower end (see figure). If a sudden jerk is given to $C$, then