Tension and weight are two different concepts related to the behavior of objects in a gravitational field.
Tension: Tension refers to the force exerted by a string, rope, or any other flexible connector when it is pulled taut. In the case of a hanging body or a simple pendulum, tension is the force exerted by the string or the suspension point that keeps the object suspended. It acts along the direction of the string and is responsible for providing the necessary centripetal force for circular motion.
Weight: Weight is the force exerted by a mass due to gravity. It is the gravitational force acting on an object and is given by the equation W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. Weight acts vertically downward and is proportional to the mass of the object.
When it comes to the period and amplitude of a hanging body or a simple pendulum:
Period: The period of a simple pendulum, which is the time taken for one complete oscillation, is not affected by tension. The period of a pendulum is determined solely by the length of the pendulum and the acceleration due to gravity, following the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. The tension in the string only affects the motion of the pendulum by providing the necessary centripetal force, but it does not directly influence the period.
Amplitude: The amplitude of a hanging body or a simple pendulum is determined by the initial displacement or angle from the equilibrium position. The tension in the string does not directly affect the amplitude of the pendulum. However, if the amplitude becomes too large, the tension in the string may become significant and affect the motion of the pendulum by deviating from the simple harmonic motion and introducing non-linear effects.
In summary, tension is the force exerted by a string or connector, while weight is the gravitational force acting on an object. Tension affects the motion of a hanging body or pendulum by providing the necessary centripetal force, but it does not influence the period. The period of a pendulum depends on its length and the acceleration due to gravity. The amplitude of a hanging body or pendulum is determined by the initial displacement and is not directly affected by tension.