In the given figure, two identical particles of mass m are tied together with an inextensible light string. The string is pulled at its center with a constant force F. The whole system lies on a smooth horizontal plane. We need to determine the motion of the particles under the influence of the pulling force.


To solve this problem, we can consider the motion of each particle separately and then analyze their combined motion.


Let's consider the motion of particle 1. Since the string is inextensible, the tension in the string will be the same at all points. Let's denote this tension as T. The net force acting on particle 1 is the tension T in the direction of the force F. Therefore, we can write the equation of motion for particle 1 as:
m * a1 = T - F


Similarly, considering the motion of particle 2, the net force acting on it is also T in the direction of the force F. Therefore, the equation of motion for particle 2 can be written as:
m * a2 = T - F


Since the two particles are tied together, their accelerations a1 and a2 will be the same. Therefore, we can write a1 = a2 = a. Substituting this into the equations of motion for particle 1 and particle 2, we get:
m * a = T - F (1)
m * a = T - F (2)


To solve these equations, we need to eliminate the tension T. We can do this by adding equation (1) and equation (2):
2m * a = 2T - 2F
2m * a = 2(T - F)
2m * a = 2T - 2F
T = F + ma


In conclusion, under the influence of the pulling force F, the tension in the string T is given by T = F + ma, where m is the mass of each particle and a is the common acceleration of the particles. This analysis helps us understand the motion of the particles tied together by an inextensible light string.