$A$ block of mass $0.18 \ kg$ is attached to a spring of force-constant $2 \ N/m$. The coefficient of friction between the block and the floor is $0.1$. Initially,the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of $0.06 \ m$ and comes to rest for the first time. The initial velocity of the block in $m/s$ is $v = N/10$. Then $N$ is:

$A$ disc of mass $0.2 \ kg$ is kept floating in air without falling by vertically firing bullets each of mass $0.05 \ kg$ on the disc at the rate of $10$ bullets per second. If the bullets rebound with the same speed,then the speed of each bullet is (Acceleration due to gravity $g = 10 \ m \ s^{-2}$) (in $m \ s^{-1}$)

Four blocks $A, B, C$ and $D$ of masses $6 \,kg, 3 \,kg, 6 \,kg$ and $1 \,kg$ respectively are connected by light strings passing over frictionless pulleys as shown in the figure. The strings $P$ and $Q$ are horizontal. The coefficient of friction between the horizontal surface and the block $B$ is $0.2$ and the blocks $A$ and $B$ move together. If the system is released from rest, then the tension in the string $Q$ is (Acceleration due to gravity, $g=10 \,ms^{-2}$) (in $\,N$)

$A$ balloon of total mass $M$ and a fixed size starts coming down with an acceleration $f$ $(f < g)$. The fraction of the total mass of the balloon which must be dropped from it so that it starts going up with an acceleration of $f$ (assuming negligible air resistance) is

Imagine a situation in which the horizontal surface of block $M_0$ is smooth and its vertical surface is rough with a coefficient of friction $\mu$. In the above problem,choose the correct value$(s)$ of $F$ for which the blocks $M$ and $m$ remain stationary with respect to $M_0$.

In the given system,if $M_2 = 2M_1$,the tension in the string is $T$. If the positions of the blocks are interchanged,what will be the new tension in the string?