Get 2 FREE Instant-Explanations on Filo with code FILOAPP

The period of oscillation of a simple pendulum is T=2 {{L}{g}

Question

Medium

Solving time: 3 mins

The period of oscillation of a simple pendulum is $T = 2 π \frac{L}{g}$ . Measured value of $L$ is $20.0 cm$ known to $1 mm$ accuracy and time for 100 oscillations of the pendulum is found to be $90 s$ using a wrist watch of 1 s resolution. The accuracy in the determination of $g$ is

2%

3%

1%

5%

Views: 5,352 students

Updated on: Sep 15, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2015

Found 3 tutors discussing this question

Elizabeth Discussed

The period of oscillation of a simple pendulum is

T = 2 π \frac{L}{g}

. Measured value of

L

20.0 cm

known to

1 mm

accuracy and time for 100 oscillations of the pendulum is found to be

90 s

using a wrist watch of 1 s resolution. The accuracy in the determination of

g

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Given time period

T = 2 π L / g

Thus, changes can be expressed as

\pm \frac{2Δ T}{T} = \pm \frac{Δ L}{L} \pm \frac{Δ g}{g}

According to the question, we can write

\frac{Δ L}{L} = \frac{0.1 cm}{20.0 cm} = \frac{1}{200}

Again time period

T = \frac{90}{100} s

and

Δ T = \frac{1}{100} S

\Rightarrow \frac{Δ T}{T} = \frac{1}{90}

Now,

∵ T = 2 π \frac{L}{g}

∵ g = 4 π^{2} \frac{L}{T ^{2}}

∴ \frac{Δ g}{g} = \frac{Δ L}{L} + \frac{2Δ T}{T}

\frac{Δ g}{g} \times 100% = (\frac{Δ L}{L}) \times 100% + (\frac{2Δ T}{T}) \times 100%

= (\frac{1}{200} \times 100) % + 2 \times \frac{1}{90} \times 100%

≃ 2.72% \approx 3%

Thus, accuracy in the determination of

g

is approx

3%

Was this solution helpful?

Report

Filo tutor solutions (8)

Learn from their 1-to-1 discussion with Filo tutors.

5 mins

Uploaded on: 6/30/2023

Ask your question, on a video call with tutor

Connect instantly with this tutor

Connect now

Taught by

Sudesh Verma

Total classes on Filo by this tutor - 16,053

Teaches : Physics, Biology, Organic Chemistry

Connect instantly with this tutor

Connect now

Notes from this class (2 pages)

Download

Was this solution helpful?

Report

8 mins

Uploaded on: 9/15/2023

Ask your question, on a video call with tutor

Connect instantly with this tutor

Connect now

Taught by

Anarudh Maurya

Total classes on Filo by this tutor - 41,473

Teaches : Physics, Mathematics

Connect instantly with this tutor

Connect now

Notes from this class (2 pages)

Download

Was this solution helpful?

132

Report

23 mins

Uploaded on: 6/30/2023

Ask your question, on a video call with tutor

Connect instantly with this tutor

Connect now

Taught by

Bipin Kumar

Total classes on Filo by this tutor - 24,935

Teaches : Physics, Mathematics, English

Connect instantly with this tutor

Connect now

Notes from this class (5 pages)

Download

Was this solution helpful?

Report

See more 1-on-1 discussions (5)

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our Physics tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	The period of oscillation of a simple pendulum is $T = 2 π \frac{L}{g}$ . Measured value of $L$ is $20.0 cm$ known to $1 mm$ accuracy and time for 100 oscillations of the pendulum is found to be $90 s$ using a wrist watch of 1 s resolution. The accuracy in the determination of $g$ is
Updated On	Sep 15, 2023
Topic	Oscillations
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 8
Upvotes	864
Avg. Video Duration	12 min

The period of oscillation of a simple pendulum is $T = 2 π \frac{L}{g}$ . Measured value of $L$ is $20.0 cm$ known to $1 mm$ accuracy and time for 100 oscillations of the pendulum is found to be $90 s$ using a wrist watch of 1 s resolution. The accuracy in the determination of $g$ is

Text solutionVerified

Filo tutor solutions (8)

Questions from JEE Mains 2015 - PYQs

Practice questions from Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Practice questions from Oscillations in the same exam

Practice more questions from Oscillations

Practice questions on similar concepts asked by Filo students

The period of oscillation of a simple pendulum is T=2πgL​​. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The accuracy in the determination of g is

Text solutionVerified

Filo tutor solutions (8)

Questions from JEE Mains 2015 - PYQs

Practice questions from Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Practice questions from Oscillations in the same exam

Practice more questions from Oscillations

Practice questions on similar concepts asked by Filo students

Related books for questions on Oscillations

Previous year question papers

The period of oscillation of a simple pendulum is $T = 2 π \frac{L}{g}$ . Measured value of $L$ is $20.0 cm$ known to $1 mm$ accuracy and time for 100 oscillations of the pendulum is found to be $90 s$ using a wrist watch of 1 s resolution. The accuracy in the determination of $g$ is