$A$ balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$). How much mass should be removed from it so that it starts moving up with an acceleration $a$?

For the given system,find the tension $T_2$ in the upper string.

Column $II$ shows five systems in which two objects are labelled as $X$ and $Y$. Also in each case a point $P$ is shown. Column $I$ gives some statements about $X$ and/or $Y$. Match these statements to the appropriate system$(s)$ from Column $II$.

Column $I$	Column $II$
$(A)$ The force exerted by $X$ on $Y$ has a magnitude $Mg$.	$(p)$ Block $Y$ of mass $M$ on a fixed inclined plane $X$,slides on it with a constant velocity.
$(B)$ The gravitational potential energy of $X$ is continuously increasing.	$(q)$ Two ring magnets $Y$ and $Z$,each of mass $M$,are kept in a frictionless vertical plastic stand. $Y$ rests on base $X$ and $Z$ hangs in equilibrium. The system is in a lift moving up with constant velocity.
$(C)$ Mechanical energy of the system $X+Y$ is continuously decreasing.	$(r)$ $A$ pulley $Y$ of mass $m_0$ is fixed to a table $X$. $A$ block of mass $M$ hangs from a string over the pulley,fixed at $P$. The system is in a lift moving down with constant velocity.
$(D)$ The torque of the weight of $Y$ about point $P$ is zero.	$(s)$ $A$ sphere $Y$ of mass $M$ is released in a non-viscous liquid $X$ and moves down.
	$(t)$ $A$ sphere $Y$ of mass $M$ is falling with terminal velocity in a viscous liquid $X$.

Block $B$ of mass $100 \ kg$ rests on a rough surface with a friction coefficient $\mu = 1/3$. $A$ rope is tied to block $B$ as shown in the figure. The maximum acceleration with which boy $A$ of mass $25 \ kg$ can climb the rope without making the block move is:

$A$ truck starting from rest moves with an acceleration of $5\,m/s^2$ for $1\,sec$ and then moves with constant velocity. The velocity w.r.t. ground v/s time graph for the block in the truck is (Assume that the block does not fall off the truck and the coefficient of friction $\mu = 0.2$):

Given in the figure are two blocks $A$ and $B$ of weight $20\ N$ and $100\ N,$ respectively. These are being pressed against a wall by a force $F$ as shown. If the coefficient of friction between the blocks is $0.1$ and between block $B$ and the wall is $0.15$,the frictional force applied by the wall on block $B$ is ........... $N$.