$A$ particle initially at rest is subjected to two forces. One is constant,the other is a retarding force proportional to the particle velocity. In the subsequent motion of the particle,

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 $a_0$,and if $a_{min}$ and $a_{max}$ are the minimum and maximum values of $a_0$ for which the blocks remain stationary with respect to the surface,then identify the correct statements.

$A$ uniform cube of side $b$ and mass $M$ rests on a rough horizontal table. $A$ horizontal force $F$ is applied normal to one of the faces at a point at a height $3b/4$ above the base. What should be the coefficient of friction $\mu$ between the cube and the table so that it will tip about an edge before it starts slipping?

In the figure,a ball of mass $m$ is tied with two strings of equal length as shown. If the rod is rotated with angular velocity $\omega$,then

$A$ mass $2 \sqrt{3} \,kg$ is acted upon by two forces which are inclined to each other at $60^{\circ}$ and each of magnitude $1 \,N$. The acceleration of that mass in $SI$ system is $\left[\sin 30^{\circ}=\cos 60^{\circ}=0.5\right]$ (in $\,m / s^{2}$)

$A$ $20 \text{ ton}$ truck is travelling along a curved path of radius $240 \text{ m}$. If the center of gravity of the truck above the ground is $2 \text{ m}$ and the distance between its wheels is $1.5 \text{ m}$, the maximum speed of the truck with which it can travel without toppling over is (Acceleration due to gravity $= 10 \text{ ms}^{-2}$) (in $\text{ ms}^{-1}$)