On a stationary sail-boat,air is blown at the sails from a fan attached to the boat. The boat will

$A$ 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]

$A$ force $F=t$ is applied to block $A$ as shown in the figure. The force is applied at $t=0$ seconds when the system was at rest and the string was just straight without tension. Which of the following graphs shows the friction force between block $B$ and the horizontal surface as a function of time $t$?

In the arrangement shown in the figure,if the blocks of masses $m$ and $2m$ are released from rest,find the tension in the string. (Given: $\mu_1 = 2/3$ for mass $m$,$\mu_2 = 1/3$ for mass $2m$,the string is massless and inextensible,and the pulley is frictionless.)

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 $M_0$.

When a body moves with some friction on a surface,