$A$ freely falling body has attained a velocity of $2 \,m/s$. If the weight of the body is now opposed by a constant upward air resistance force equal to its weight, what is the total distance travelled by the body before it comes to rest (in $\,m$)?

$A$ small block of mass $m$ is placed on a wedge of mass $M$ as shown,which is initially at rest. All the surfaces are frictionless. The spring attached to the other end of the wedge has force constant $k$. If $a'$ is the acceleration of $m$ relative to the wedge as it starts coming down and $A$ is the acceleration acquired by the wedge as the block starts coming down,then

$A$ mass of $2 \, kg$ is suspended with a thread $AB$ as shown in the figure. $A$ thread $CD$ of the same type is attached to the other end of the $2 \, kg$ mass. The lower thread is pulled gradually,harder and harder in the downward direction,so as to apply force on $AB$. Which of the threads will break and why?

$A$ monkey of mass $40 \, kg$ climbs on a rope which can stand a maximum tension of $600 \, N$. In which of the following cases will the rope break: the monkey
$(a)$ climbs up with an acceleration of $6 \, m \, s^{-2}$
$(b)$ climbs down with an acceleration of $4 \, m \, s^{-2}$
$(c)$ climbs up with a uniform speed of $5 \, m \, s^{-1}$
$(d)$ falls down the rope nearly freely under gravity? (Ignore the mass of the rope).

Two bodies of masses $10\; kg$ and $20\; kg$ respectively,kept on a smooth horizontal surface,are tied to the ends of a light string. $A$ horizontal force $F = 600\; N$ is applied to $(i)\; A$,$(ii)\; B$ along the direction of the string. What is the tension in the string in each case?

Two blocks of mass $M_1 = 20\,kg$ and $M_2 = 12\,kg$ are connected by a metal rod of mass $8\,kg$. The system is pulled vertically up by applying a force of $480\,N$ as shown. The tension at the mid-point of the rod is ........ $N$.