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:

$A$ balloon of mass $M$ descends with an acceleration $a (< g)$. What mass needs to be removed from the balloon so that it starts ascending with acceleration $a$?

Two particles of equal mass $m$ are connected to a rope $AB$ of negligible mass such that one is at end $A$ and the other divides the length of the rope in the ratio $1:2$ from $B$. The rope is rotated about end $B$ in a horizontal plane. The ratio of the tension in the smaller part (between $B$ and the middle particle) to the tension in the larger part (between the two particles) is (ignore the effect of gravity).

The mass of a lift is $500\, kg$. When it ascends with an acceleration of $2\, m/s^2$,the tension in the cable will be........... $N$ $[g = 10\, m/s^2]$

$A$ 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

The figure shows a uniform rod of length $30 \,cm$ having a mass of $3.0 \,kg$. The rod is pulled by constant forces of $20 \,N$ and $32 \,N$ as shown. Find the force exerted by the $20 \,cm$ part of the rod on the $10 \,cm$ part (all surfaces are smooth).