$A$ particle of mass $7 \, kg$ moving at $5 \, m/s$ is acted upon by a variable force opposite to its initial direction of motion. The variation of force $F$ with time $t$ is shown in the graph.

$A$ block of mass $2M$ is attached to a massless spring with spring-constant $k$. This block is connected to two other blocks of masses $M$ and $2M$ using two massless pulleys and strings. The accelerations of the blocks are $a_1, a_2$ and $a_3$ as shown in the figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is $x_0$. Which of the following option$(s)$ is/are correct? [$g$ is the acceleration due to gravity. Neglect friction]

$A$ plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^o$,the box starts to slip and slides $4.0\, m$ down the plank in $4.0\, s$. The coefficients of static and kinetic friction between the box and the plank will be,respectively:

$Assertion$: Two bodies of masses $M$ and $m$ $(M > m)$ are allowed to fall from the same height. If the air resistance for each is the same,then both bodies will reach the Earth simultaneously.
$Reason$: For the same air resistance,the acceleration of both bodies will be the same.

Two balls of masses $m_1$ and $m_2$ are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly,the powder charge explodes and the masses are pushed apart. The mass $m_1$ travels a distance $s_1$ and stops. If the coefficients of friction between the balls and the ground are the same,the mass $m_2$ stops after travelling the distance:

Two blocks,$4\, kg$ and $2\, kg$,are sliding down an inclined plane as shown in the figure. The acceleration of the $2\, kg$ block is ........ $m/s^2$.