### Motion of Two Bodies Connected by a String over a pulley

Motion of Two Bodies Connected by a String over a pulley on different planes.

Consider a light inextensible string passing over a smooth pulley, as shown in Fig. 1.25, so that the tension (T) in both the strings is same.
Let mass m1 is greater than mass m2. Since the string is inextensible, the upward acceleration of mass m2 will be equal to the downward acceleration of mass m1. This acceleration is given by

and tension in the string,

Let us now consider the following cases of motion of two bodies connected by a string.

1. First of all, let us consider the motion of two bodies connected by an inextensible string, one of which is hanging freely and the other is lying on a smooth horizontal plane as shown in Fig. 1.26.
Since the string is inextensible, the tension (T) in both the strings will be equal . The acceleration of the system is given by

and

2. If instead of smooth plane, it is a rough horizontal plane, as shown in Fig, 1.27, then frictional force equal to:

will act in the opposite direction to the motion of mass m2, where u is the coefficient of friction. In such a case,

3. When the plane is a smooth inclined plane, as shown in Fig. 1.28, then

4. When the plane is a rough inclined plane, as shown in Fig. 1.29, then

### Are Engineers Favourite Among Girls?

What do girls think about men who are engineers and what type of engineers are most favourite among girls? A survey was conducted by a team of aboutmech with members chosen from different countries. Each team member carried out a neutral survey in his/ her country to evaluate what females think about most of the engineers from different engineering branches. An overview of different questions asked in survey is given below: Question: Which male engineers do you find more attractive as a husband? Almost 50% women voted for mechanical engineers to be the most attractive husbands among other engineers. So mechanical engineers are most favourite among girls as a husband. They find them more trustworthy, intelligent, and creative. A married women from California said, “If your husband is a mechanical engineer, he will help you in everyday tasks. Because mechanical engineers are good team players and they have creative ideas about everything.” Which male engineers do you find more