If the breaking strength of a rope is $\frac{4}{3}$ times the weight of a person,then the maximum acceleration with which the person can safely climb up the rope is ($g$ = acceleration due to gravity).

Two particles each of mass $m$ are moving in horizontal circles with the same angular speed $\omega$. If both strings are of the same length $l$,find the ratio of tension in the strings $\frac{T_1}{T_2}$.

$A$ bar of mass $m$ resting on a smooth horizontal plane starts moving due to a constant force $F$. In the process of its rectilinear motion,the angle $\theta$ between the direction of this force and the horizontal varies as $\theta = k x$,where $k$ is a constant and $x$ is the distance traversed by the bar from its initial position. The velocity $(v)$ of the bar as a function of the angle $\theta$ is

An elevator of mass $m$ is connected to a rope which pulls the elevator up with a maximum acceleration equal to $a$. If the maximum bearable tension in the rope is $T$,then for a safe journey the minimum diameter of the rope is $[g=$ acceleration due to gravity$]$

Two blocks of mass $8\,kg$ and $2\,kg$ are connected by a string and they are released on an inclined plane of inclination $30^o$ as shown in the figure. What will be the tension in the string connecting the two blocks (in $,N$)? (Assume the surface is frictionless and $g = 10\,m/s^2$)

The mass of a lift is $500\, kg$. When it ascends with an acceleration of $2\, m/s^2$,the tension in the cable will be........... $N$ $[g = 10\, m/s^2]$