f M and m are particles connected by light inextensible string. M is held at center and
rotated about horizontal axis as M is in equilibrium.What is torque ABOUT ITS CENTER
To find the torque about the center of the system, we first need to understand the concept of torque. Torque is the measure of the tendency of a force to rotate an object around an axis. Mathematically, torque is defined as the cross product of the force vector and the vector connecting the axis of rotation to the point where the force is applied.
In this scenario, we have an inextensible string connecting two particles, M and m. M is held at the center and rotated about a horizontal axis in equilibrium. Since the string connecting M and m is inextensible, both particles will rotate about the same axis.
To find the torque about the center, we need to consider the forces acting on the system. There are two forces acting on the system: the weight of M and m, and the tension in the string. The weight of M and m can be considered as acting at their respective centers of mass.
Since M is in equilibrium, the torques due to the weight of M and m will cancel out. Therefore, the torque about the center of the system is only due to the tension in the string.
To calculate the torque due to the tension in the string, we need to consider the magnitude of the tension force and the distance between the axis of rotation (center) and the point where the force is applied. The torque can be calculated using the formula:
Torque = Tension * Perpendicular Distance
where Tension is the magnitude of the tension force and Perpendicular Distance is the shortest distance between the axis of rotation (center) and the line of action of the force.
In this case, as M is held at the center, the distance between the axis of rotation and the point where the tension force is applied becomes zero. Therefore, the torque about the center is zero.
To summarize, the torque about the center of the system is zero as M is held at the center and is in equilibrium.