Three blocks of masses $m_1, m_2$ and $m_3$ are connected by massless strings as shown on a frictionless table. They are pulled with a force $F = 40 \, N$. If $m_1 = 10 \, kg, m_2 = 6 \, kg$ and $m_3 = 4 \, kg$,the tension $T_2$ (between $m_1$ and $m_2$) will be ........ $N$.

At $t = 0$, a body of mass $100 \text{ g}$ starts moving under the influence of a force $(5\hat{i} + 10\hat{j}) \text{ N}$. After $2 \text{ s}$, its position is $(2x\hat{i} + 5y\hat{j}) \text{ m}$. The ratio $x : y$ is . . . . . . .

Three blocks of masses $3\, kg, 2\, kg$,and $1\, kg$ are placed side by side on a smooth surface as shown in the figure. $A$ horizontal force of $12\, N$ is applied to the $3\, kg$ block. The net force on the $2\, kg$ block is ............ $N$.

$A$ block of mass $M$ on a horizontal smooth surface is pulled by a load of mass $M/2$ by means of a rope $AB$ and string $BC$ as shown in the figure. The length and mass of the rope $AB$ are $L$ and $M/2$ respectively. As the block is pulled from $AB = L$ to $AB = 0$,its acceleration changes from:

Three identical particles of mass $m$ are joined together by a thread as shown in the figure. All three particles are moving in a horizontal plane in a circle about the point $O$. If the velocity of the outermost particle is $v_0$,then the ratio of tensions in the three sections of the string is:

On a smooth plane surface,two blocks $A$ and $B$ are accelerated by applying a force of $15 \, N$ on block $A$. If the mass of block $B$ is twice that of block $A$,the force on block $B$ is ........... $N$.