If $4 \mathrm{N}$ and $9 \mathrm{N}$ forces are acting perpendicular to an object. Then determine the resultant force.

A flexible chain of weight W hangs between two fixed points $A$ and $B$ which are at the same horizontal level. The inclination of the chain with the horizontal at both the point supports is $\theta$. What is the tension in the chain at the midpoint?

In figure given below, masses $m_1, m_2$, and $M$ are $20 \mathrm{kg}$, $5 \mathrm{kg}$ and $50 \mathrm{kg}$ respectively. The coefficient of friction between $M$ and ground is zero. The coefficient of friction between $m_1$ and $M$ and that between $m_2$ and ground is $0.3$. The pulleys and the strings are massless. The string is perfectly horizontal between $P_1$ and $m_1$ and also between $P_2$ and $m_2$. The string is perfectly vertical between $P_1$ and $P_2$. An external horizontal force $F$ is applied to the mass $M$. (Take $g = 10 m/s^2$).

 Let the magnitude of the force of friction between $m_1$ and $M$ be $f_1$ and that between $m_2$ and ground be $f_2$. For a particular force $F$ it is found that $f_1 = 2f_2$. Find $f_1$ and $f_2$. Write equations of motion of all the masses. Find $F$, the tension in the string and accelerations of the masses.