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 ........... $N$.

Two particles each of mass $m$ are moving in horizontal circles with the same angular speed $\omega$. If both strings are of the same length $l$,find the ratio of tension in the strings $\frac{T_1}{T_2}$.

The mass of a lift is $2000 \, kg$. When the tension in the supporting cable is $28000 \, N$,then its acceleration is:

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 . . . . . . .

$A$ dynamometer $D$ is attached to two blocks of masses $6 \, kg$ and $4 \, kg$ as shown in the figure. The reading of the dynamometer is ............ $N$.

$A$ block of mass $M$ is placed on a horizontal surface and is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. If the surface between $M$ and $m_0$ has a coefficient of friction $\mu$,find the tension in the string,assuming the system moves together.