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 $A$ and $B$,each of mass $M$,are connected by a massless spring. $A$ force $F$ acts on the mass $B$ as shown in the figure. If the mass $A$ starts moving away from mass $B$ with acceleration $a$,then the acceleration of mass $B$ will be:

$A$ cord is used to lower vertically a block of mass $M$ by a distance $d$ with constant downward acceleration $\frac{g}{4}$. Work done by the cord on the block is

Two rectangular blocks of masses $40 \ kg$ and $60 \ kg$ are connected by a string and kept on a frictionless horizontal table. If a force of $1000 \ N$ is applied on the $60 \ kg$ block away from the $40 \ kg$ block,then the tension in the string is: (in $N$)

$A$ force $F = 10t$ acts on a block of mass $10 \, kg$ as shown in the figure. Find the time $t$ when the block loses contact with the surface.

$A$ 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 $N$)