$A$ block of mass $m$ moves on a horizontal rough surface with initial velocity $v$. The height of the centre of mass of the block is $h$ from the surface. Consider a point $A$ on the surface.

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:

Two pulley arrangements shown in the figure are identical. The mass of the rope is negligible. In figure $(a)$,the mass $m$ is lifted by attaching a mass $2m$ to the other end of the rope. In figure $(b)$,$m$ is lifted up by pulling the other end of the rope with a constant downward force $F = 2mg$. The accelerations of $m$ in the two cases are respectively:

Three blocks with masses $m$,$2m$,and $3m$ are connected by strings,as shown in the figure. After an upward force $F$ is applied on block $m$,the masses move upward at a constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)

$A$ particle of mass $m$ is acted upon by a force $F$ given by the empirical law $F = \frac{R}{t^2} v(t)$. If this law is to be tested experimentally by observing the motion starting from rest,the best way is to plot:

Imagine the situation in which the given arrangement is placed inside a trolley that can move only in the horizontal direction,as shown in the figure. If the trolley is accelerated horizontally along the positive $x$-axis with $a_0$,then identify the correct statement$(s)$ related to the tension $T$ in the string.