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 $\frac{T_1}{T_2}$.

$A$ small ball $B$ of mass $m$ is suspended with a light inelastic string of length $L$ from a block $A$ of the same mass $m$,which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by an angle $\theta$ from the equilibrium position and then released. The maximum velocity of the block during the subsequent motion of the system after the release of the ball is

The mass of the lift is $200 \ kg$. When it ascends with an acceleration of $4 \ m/s^2$,the tension in the cable supporting the lift will be [Given: Acceleration due to gravity $g = 10 \ m/s^2$]. (in $N$)

Three blocks of masses $2 \, kg, 3 \, kg$ and $5 \, kg$ are connected to each other with light strings and are placed on a frictionless surface as shown in the figure. The system is pulled by a force $F = 10 \, N$. Find the tension $T_1$ in the string between the $2 \, kg$ and $3 \, kg$ blocks. (in $, N$)

$A$ block of mass $m_1$ rests on a horizontal table. $A$ string tied to the block is passed over a frictionless pulley fixed at the end of the table,and to the other end of the string is hung another block of mass $m_2$. The acceleration of the system is

An $80\, kg$ person is parachuting and is experiencing a downward acceleration of $2.8\, m/s^2$. The mass of the parachute is $5\, kg$. The upward force on the open parachute is ........... $N$ (Take $g = 9.8\, m/s^2$)