Three masses of $1\, kg$,$6\, kg$,and $3\, kg$ are connected to each other with threads and are placed on a table as shown in the figure. The acceleration with which the system is moving is $....... \, ms^{-2}$. (Take $g = 10\, ms^{-2}$)

In the arrangement shown in the figure, the work done by the string on the block of mass $0.36 \,kg$ during the first second after the blocks are released from a state of rest is: (Ignore friction and the mass of the string.)
(Acceleration due to gravity, $g = 10 \,m/s^2$) (in $\,J$)

Tension in the rope at the rigid support is ............ $N$ $\left(g=10 \,m / s ^2\right)$

In the figure,the mass of a ball is $\frac{9}{5}$ times the mass of the rod. The length of the rod is $1 \, m$. The initial level of the ball is the same as the lower end of the rod. Find the time taken by the ball to reach the upper end of the rod. (in $s$)

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the center $P$ (as shown in the figure). Now,the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result,the particles move towards each other on the surface. The magnitude of acceleration,when the separation between them becomes $2x$ is

Two masses of $5 \ kg$ and $10 \ kg$ are suspended from a massless pulley as shown in the figure. Calculate the acceleration of the system when the masses are left free.