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 $\frac{T_1}{T_2}$.

Two masses of $4\, kg$ and $5 \,kg$ are connected by a string passing through a frictionless pulley and are kept on a frictionless table as shown in the figure. The acceleration of the $5\, kg$ mass is ........... $m/s^2$.

Two blocks of masses $m$ and $2m$ kept on a frictionless horizontal surface are connected by a massless string. Two horizontal forces $F_1 = (4.2t) \text{ N}$ and $F_2 = (7.5t) \text{ N}$,where '$t$' is time in seconds,are acting on the system as shown in the figure. The time at which the tension in the string between the two blocks becomes $10.6 \text{ N}$ is $t$ seconds.

$A$ small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force $mkv^{2}$ where $v$ is its speed. The maximum height attained by the ball is

If all surfaces are smooth,then the acceleration of mass $m_2$ will be $-$

$A$ balloon of mass $M$ descends with an acceleration $a (< g)$. What mass needs to be removed from the balloon so that it starts ascending with acceleration $a$?