Why the mesaure of the sphere doesn't play a part at the pendulum???
IT is because in a pendelum, the force of gravity on the inertia of the mass is countered exactly as it falls, and rises. If the sphere is larger, it has a larger force going downward, but it also has a larger force retarding it going up. The mass of the sphere is irrevelent in considering the change of motion (acceleartion) as the gravity force is directly proportional to Mass, but acceleartion is inversly proportional to mass, ie, acceleration=constant*Mass/Mass
thanks a lot
To understand why the measure, or size, of a sphere does not affect the motion of a pendulum, it is important to know the fundamental concepts behind pendulum motion.
A pendulum is a simple mechanical system consisting of a mass (typically a bob or a weight) attached to a fixed point by a string or rod. When released from a certain angle, the pendulum swings back and forth under the influence of gravity.
The motion of a pendulum is primarily influenced by two factors: the length of the pendulum and the acceleration due to gravity. The length of the pendulum refers to the distance between the fixed point (or pivot) and the center of mass of the bob. The acceleration due to gravity is a constant value that depends on the location on Earth.
The mass of the bob, including its size or volume, does not significantly affect the motion of the pendulum. This principle is known as the equivalence principle, which states that for small oscillations, the period of a pendulum (the time taken to complete one swing back and forth) is independent of the mass or size of the bob.
The reason for this is that both the gravitational force and the inertial force (force due to the motion of the pendulum) act on the center of mass of the bob. The size or volume of the bob does not alter the way these forces act on it, as long as the mass remains the same.
To calculate the period of a pendulum, you only need to know the length of the pendulum (L) and the acceleration due to gravity (g). The formula for the period (T) is given by:
T = 2π * √(L/g)
As you can see, there is no term for the size or measure of the bob in this equation, further confirming that it does not play a significant role in the motion of a pendulum.
In summary, the size or measure of a sphere that serves as a bob in a pendulum does not affect its motion because the period of the pendulum is determined solely by its length and the acceleration due to gravity.