Two bodies of mass $4 \, kg$ and $6 \, kg$ are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity $(g)$ is

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 masses $M_1$ and $M_2$ are accelerated uniformly on a frictionless surface as shown in the figure. The ratio of the tensions $T_1/T_2$ is:

In the figure,the tension in the diagonal string is $60\,N$. Find the magnitude of the horizontal forces $F_1$ and $F_3$ that must be applied to hold the system in the position shown.

In the system shown in the figure,there is no friction anywhere. The block $C$ $(2 \, kg)$ moves down by a distance $x_0 = 10 \, cm$ with respect to the wedge $D$ $(4 \, kg)$ when the system is released from rest. The velocity of $A$ $(1 \, kg)$ with respect to $B$ $(1 \, kg)$ will be $(g = 10 \, m/s^2)$ ......... $m/s$.

If $m_1 = 4m_2$ and the acceleration of $m_1$ is $a$,find the tension $T$ in the string.