(D) The time period $T$ is given by $T = \frac{t}{n}$,where $t = 40 \ s$ and $n = 20$.Given the least count of the stopwatch is $\Delta t = 1 \ s$.The

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) The time period $T$ is given by $T = \frac{t}{n}$,where $t = 40 \ s$ and $n = 20$.Given the least count of the stopwatch is $\Delta t = 1 \ s$.The error in the time period $T$ is $\Delta T = \frac{\Delta t}{n} = \frac{1 \ s}{20} = 0.05 \ s$. Thus,statement $(A)$ is true.The formula for acceleration due to gravity is $g = \frac{4 \pi^2 L}{T^2}$.The relative error in $g$ is $\frac{\Delta g}{g} = 2 \frac{\Delta T}{T}$.Substituting the values: $\frac{\Delta g}{g} = 2 \times \frac{0.05}{2} = 0.05$.Percentage error in $g = \frac{\Delta g}{g} \times 100 = 0.05 \times 100 = 5 \%$. Thus,statement $(C)$ is true.

Class 11 Physics Units, Dimensions and Measurement Errors of Measurement

Difficult

$A$ student uses a simple pendulum of exactly $1 \ m$ length to determine $g$,the acceleration due to gravity. He uses a stopwatch with a least count of $1 \ s$ for this and records $40 \ s$ for $20$ oscillations. For this observation,which of the following statement$(s)$ is (are) true?
$(A)$ Error $\Delta T$ in measuring $T$,the time period,is $0.05 \ s$
$(B)$ Error $\Delta T$ in measuring $T$,the time period,is $1 \ s$
$(C)$ Percentage error in the determination of $g$ is $5 \%$
$(D)$ Percentage error in the determination of $g$ is $2.5 \%$

IIT 2010 All IIT

A
$(B, D)$
B
$(A, D)$
C
$(C, D)$
D
$(A, C)$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Units, Dimensions and Measurement

Subtopic

Errors of Measurement

Previous Year

IIT 2010 Paper All IIT years →

$A$ cylindrical wire has a mass $(0.3 \pm 0.003) \text{ g}$,radius $(0.5 \pm 0.005) \text{ mm}$ and length $(6 \pm 0.06) \text{ cm}$. The maximum percentage error in the measurement of its density is (in $\%$)

EasyKCET 2020

View Solution

If $P = \frac{A^3}{B^{5/2}}$ and $\Delta A$ is the absolute error in $A$ and $\Delta B$ is the absolute error in $B$,then the absolute error $\Delta P$ in $P$ is:

Easy

View Solution

Two resistances are measured in $\Omega$ and are given as $R_1 = 3 \Omega \pm 1\%$ and $R_2 = 6 \Omega \pm 2\%$. When they are connected in parallel,the percentage error in equivalent resistance is .......... $\%$

Difficult

View Solution

The resistance $R = \frac{V}{I}$,where $V = (50 \pm 2) \; V$ and $I = (20 \pm 0.2) \; A$. The percentage error in $R$ is $x\%$. The value of $x$ to the nearest integer is .........

MediumJEE MAIN 2021

View Solution

$A$ physical quantity $S$ is related to four observables $a, b, c$, and $d$ as $S = \frac{\sqrt{a} b}{c^3 d^4}$. If the percentage errors of measurement in $a, b, c$, and $d$ are $2 \%$, $1 \%$, $1 \%$, and $1 \%$ respectively, then the percentage error in the quantity $S$ is: (in $\%$)

EasyTS EAMCET 2022

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

$A$ cylindrical wire has a mass $(0.3 \pm 0.003) \text{ g}$,radius $(0.5 \pm 0.005) \text{ mm}$ and length $(6 \pm 0.06) \text{ cm}$. The maximum percentage error in the measurement of its density is (in $\%$)

If $P = \frac{A^3}{B^{5/2}}$ and $\Delta A$ is the absolute error in $A$ and $\Delta B$ is the absolute error in $B$,then the absolute error $\Delta P$ in $P$ is:

Two resistances are measured in $\Omega$ and are given as $R_1 = 3 \Omega \pm 1\%$ and $R_2 = 6 \Omega \pm 2\%$. When they are connected in parallel,the percentage error in equivalent resistance is .......... $\%$

The resistance $R = \frac{V}{I}$,where $V = (50 \pm 2) \; V$ and $I = (20 \pm 0.2) \; A$. The percentage error in $R$ is $x\%$. The value of $x$ to the nearest integer is .........

$A$ physical quantity $S$ is related to four observables $a, b, c$, and $d$ as $S = \frac{\sqrt{a} b}{c^3 d^4}$. If the percentage errors of measurement in $a, b, c$, and $d$ are $2 \%$, $1 \%$, $1 \%$, and $1 \%$ respectively, then the percentage error in the quantity $S$ is: (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module