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 . . . . . . .

Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface. The acceleration of mass $m$ is:

The tension in the string connecting the blocks as shown in the figure is ............ $N$.

$A$ bar of mass $m$ resting on a smooth horizontal plane starts moving due to a constant force $F$. In the process of its rectilinear motion,the angle $\theta$ between the direction of this force and the horizontal varies as $\theta = k x$,where $k$ is a constant and $x$ is the distance traversed by the bar from its initial position. The velocity $(v)$ of the bar as a function of the angle $\theta$ is

The minimum acceleration with which a fireman can slide down a rope of breaking strength two-third of his weight is

$A$ constant horizontal force $\overrightarrow{F}$ of magnitude $10 \,N$ is applied to a block $A$ and this produces an acceleration of magnitude $20 \,m/s^2$. If this block $A$ is then kept against another block $B$ of mass $1.5 \,kg$ as shown in the figure and a force $F^{\prime}$ of $20 \,N$ is applied,find the force on the block $B$. Neglect friction. (in $N$)