Question

On which of the following factors the period of a pendulum does not depend ?

• A. Length of the pendulum
• B. Mass of the bob
• C. Acceleration due to gravity
• D. Amplitude of oscillations
• E. Material of the bob

Answer 1

Answer: (B), (D), (E)

Mass of the bob
Amplitude of oscillations
Material of the bob

$\text{Explanation:-}$We can se that the restoring force F from a pendulum at an angle $\theta ,$

$F=-mgsin\theta$

$\Rightarrow F=-mg\theta \left(Forsmall\theta \right)$

Now $\theta =\frac{x}{l}$

$\Rightarrow F=-mg\frac{\theta x}{l}$

$m\frac{d^{2}x}{d{t}^2}=-mg\frac{\theta x}{l}$

$\frac{d^{2}x}{d{t}^2}=\frac{gx\theta }{l}$

which represent Simple harmonic motion

With $w$ = $\sqrt{\frac{g}{l}}$

Now, $T=\frac{2\pi }{w}$

$\Rightarrow T=2\pi \sqrt{\frac{l}{g}}$

$\text{Hence,}$

$Massofthebob$

$Amplitudeofoscillations$

$Materialofthebob$