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.

If $m_1 = 4m_2$,and the acceleration of $m_1$ is $a$,then find $a$.

Both the blocks shown in the figure have mass $m$ and are moving with constant velocity in the directions indicated. They are in a resistive medium which exerts an equal constant force $F$ on both blocks in the direction opposite to their velocity. The tension in the string connecting them is: (Neglect friction)

For the system shown in the figure,the pulleys are light and frictionless. The tension in the string will be

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 of masses $m_1$ and $m_2$ are suspended from the ends of a light string passing over a smooth fixed pulley. If the pulley is pulled up with an acceleration $a_0 = g$, then the tension in the string will be