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........... $N$ $[g = 10\, m/s^2]$

Three blocks of masses $4 \ kg$, $2 \ kg$, and $1 \ kg$ respectively are in contact on a frictionless table as shown in the figure. If a force of $14 \ N$ is applied on the $4 \ kg$ block, the contact force between the $4 \ kg$ and the $2 \ kg$ block will be: (in $N$)

$A$ uniform rope of mass $1.0\, kg$ is connected to a box of mass $2.0\, kg$,which is placed on a smooth horizontal surface. The free end of the rope is pulled horizontally by a force of $6\, N$. Find the tension at the midpoint of the rope in $N$.

Two blocks $A$ and $B$ of mass $m$ and $2m$ respectively are connected by a massless spring of force constant $k$. They are placed on a smooth horizontal plane. The spring is stretched by an amount $x$ and then released. The relative velocity of the blocks when the spring comes to its natural length 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 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 $\frac{T_1}{T_2}$.