Two masses $m_1 = 5\, kg$ and $m_2 = 4.8\, kg$ tied to a string are hanging over a light frictionless pulley. The acceleration of the masses when they are free to move is $...........\, m/s^2$. $(g = 9.8\, m/s^2)$

Two masses $M_{1}$ and $M_{2}$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_{2}$ is twice that of $M_{1}$,the acceleration of the system is $a_{1}$. When the mass $M_{2}$ is thrice that of $M_{1}$,the acceleration of the system is $a_{2}$. The ratio $\frac{a_{1}}{a_{2}}$ will be:

Two blocks $A$ and $B$, each of mass $20 \,kg$, lying on a frictionless table, are connected by a light string. The system is pulled horizontally with an acceleration of $2 \,ms^{-2}$ by a force $F$ applied on block $B$. The tension in the string will be: (in $\,N$)

$A$ pendulum bob of mass $50 \,g$ is suspended from the ceiling of an elevator. The tension in the string if the elevator goes up with uniform velocity is approximately .......... $N$.

$A$ smooth massless string passes over a smooth fixed pulley. Two masses $m_{1}$ and $m_{2}$ $(m_{1} > m_{2})$ are tied at the two ends of the string. The masses are allowed to move under gravity starting from rest. The total external force acting on the two masses is

$A$ block of mass $M$ is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force $F$. The kinetic energy of the block increases by $20\,J$ in $1\,s$.