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(a) The effect of the mass,m, of the cord attached to the bob, of mass M, of a pendulum is to increases the period over that for a simple pendulum is to increase the period over that for a simple pendulum in which m = 0. Make this plausible, (b) Although the effect of the mass of the cord on the pendulum is increase its period, a cord of length L swinging without anything on the end (M = 0) has a period less than that of a simple pendulum of length L. Make that plausible.
3 years ago

Answers : (1)

Jitender Pal
askIITians Faculty
365 Points
							(a)
The period T of a simple pendulum is defined as,
T = 2π√L/g
Here L is the length of the pendulum and g is the free fall acceleration.
So, the period of the simple pendulum is independent of the mass m of the suspended particle.
Thus the mass, m, of the cord attached to the bob, of mass M, of a pendulum will not affect the period over that for a simple pendulum in which m=0.
(b)
In a simple pendulum, the period T will be,
T = 2π√L/g
Here L is the length of the pendulum and g is the free fall acceleration.
The period of the simple pendulum is independent of the mass m of the suspended particle.
A simple pendulum is an idealized body consisting of a particle having mass M, suspended by a light inextensible cord. When pulled to one side of its equilibrium position and released, the pendulum swings in a vertical plane under the influence of gravity. The motion is periodic and oscillatory. As here, a cord of length L swinging without anything on the end (M=0), therefore, it will not an ideal simple pendulum anymore. Because, an ideal pendulum always contain a particle having mass M suspended by a light inextensible cord
3 years ago
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