$A$ block $A$ of mass $7 \, kg$ is placed on a frictionless table. $A$ thread tied to it passes over a frictionless pulley and carries a body $B$ of mass $3 \, kg$ at the other end. The acceleration of the system is .......... $m \, s^{-2}$ (given $g = 10 \, m \, s^{-2}$).

Two spheres $P$ and $Q$,each of mass $200 \text{ g}$,are attached to a string of length $1 \text{ m}$ as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that between $P$ and $O$ is (where $P$ is at the mid-point of the line joining $O$ and $Q$).

$A$ mass $1\, kg$ is suspended by a thread. It is
$(i)$ lifted up with an acceleration $4.9\, m/s^2$
$(ii)$ lowered with an acceleration $4.9\, m/s^2$.
The ratio of the tensions is

If a ship of mass $4 \times 10^{7} \,kg$ initially at rest is pulled by a force of $5 \times 10^{4} \,N$ through a distance of $4 \,m$, then the speed of the ship will be (resistance due to water is negligible). (in $\,ms^{-1}$)

$A$ block of mass $m$ slides on a wooden wedge,which in turn slides backward on a horizontal surface. The acceleration of the block with respect to the wedge is: Given $m = 8 \, kg, M = 16 \, kg$. Assume all surfaces shown in the figure to be frictionless.

$A$ body of mass $8\,kg$ is hanging from another body of mass $12\,kg$. The combination is being pulled upward by a string with an acceleration of $2.2\,m/s^2$. The tensions $T_1$ and $T_2$ will be respectively: