
The periodic time of a simple pendulum of length 1 m and amplitude 2 cm is 5 seconds. If the amplitude is made 4 cm, its periodic time in seconds will be
\[\begin{align}
& \text{A}.\text{ }2.5 \\
& \text{B}.\text{ }5 \\
& \text{C}.10 \\
& \text{D}.\text{ }5\sqrt{2} \\
\end{align}\]
Answer
483.6k+ views
Hint: The time period of a simple pendulum is the time taken by a pendulum to complete one full oscillation. The maximum displacement of the bob in the pendulum is the amplitude of that pendulum.
Formula used:
Time period of a simple pendulum,
$T=2\pi \sqrt{\dfrac{l}{g}}$ .
Complete step by step answer:
In the question we are given the length of the pendulum,$l$ = 1 m
Amplitude of the pendulum, A = 2cm
And the time period of this pendulum, T = 5 seconds.
We have to find the time period of this pendulum, when its amplitude becomes 4 cm.
We know, time period of a simple pendulum is given by the equation,
$T=2\pi \sqrt{\dfrac{l}{g}}$ , where ‘$l$’ is the length of the pendulum and ‘g’ is acceleration due to gravity.
From this equation, it is clear that the time period of a simple pendulum does not depend on its amplitude.
In the question, we change the amplitude of the pendulum from 2 cm to 4 cm. Length of the pendulum remains the same and acceleration due to gravity; ‘g’ is a constant.
Therefore, the time period of the pendulum when its amplitude = 4cm, length ‘$l$’=1 m will be 5 seconds.
So, the correct answer is “Option B”.
Note:
Time period of simple pendulum
For a simple pendulum, we know its angular frequency $\omega $ is given by
$\omega =\sqrt{\dfrac{g}{l}}$ , where ‘$l$’ is the length of the pendulum and ‘g’ is acceleration due to gravity.
Time period of an oscillation is generally expressed as,
$T=\dfrac{2\pi }{\omega }$ , where ‘T’ is the time period and ‘$\omega $’ is the angular frequency of the pendulum.
By substituting the value of angular frequency (ω) in the above equation, we get
$T=2\pi \sqrt{\dfrac{l}{g}}$
Therefore the time period of a pendulum is, $T=2\pi \sqrt{\dfrac{l}{g}}$
Formula used:
Time period of a simple pendulum,
$T=2\pi \sqrt{\dfrac{l}{g}}$ .
Complete step by step answer:
In the question we are given the length of the pendulum,$l$ = 1 m
Amplitude of the pendulum, A = 2cm
And the time period of this pendulum, T = 5 seconds.
We have to find the time period of this pendulum, when its amplitude becomes 4 cm.
We know, time period of a simple pendulum is given by the equation,
$T=2\pi \sqrt{\dfrac{l}{g}}$ , where ‘$l$’ is the length of the pendulum and ‘g’ is acceleration due to gravity.
From this equation, it is clear that the time period of a simple pendulum does not depend on its amplitude.
In the question, we change the amplitude of the pendulum from 2 cm to 4 cm. Length of the pendulum remains the same and acceleration due to gravity; ‘g’ is a constant.
Therefore, the time period of the pendulum when its amplitude = 4cm, length ‘$l$’=1 m will be 5 seconds.
So, the correct answer is “Option B”.
Note:
Time period of simple pendulum
For a simple pendulum, we know its angular frequency $\omega $ is given by
$\omega =\sqrt{\dfrac{g}{l}}$ , where ‘$l$’ is the length of the pendulum and ‘g’ is acceleration due to gravity.
Time period of an oscillation is generally expressed as,
$T=\dfrac{2\pi }{\omega }$ , where ‘T’ is the time period and ‘$\omega $’ is the angular frequency of the pendulum.
By substituting the value of angular frequency (ω) in the above equation, we get
$T=2\pi \sqrt{\dfrac{l}{g}}$
Therefore the time period of a pendulum is, $T=2\pi \sqrt{\dfrac{l}{g}}$
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Glucose when reduced with HI and red Phosphorus gives class 11 chemistry CBSE

The highest possible oxidation states of Uranium and class 11 chemistry CBSE

Find the value of x if the mode of the following data class 11 maths CBSE

Which of the following can be used in the Friedel Crafts class 11 chemistry CBSE

A sphere of mass 40 kg is attracted by a second sphere class 11 physics CBSE

Trending doubts
10 examples of friction in our daily life

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

Write down 5 differences between Ntype and Ptype s class 11 physics CBSE
