Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is 0 . 5 mm . The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below. Measurement condition Main scale reading Circular scale reading Two arms of gauge touching each other without wire 0 division 4 divisions Attempt- 1 : With wire 4 divisions 20 divisions Attempt- 2 : With wire 4 divisions 16 divisions What are the diameter and cross-sectional area of the wire measured using the screw gauge?

2 . 14 ± 0 . 02 mm , π 1 . 14 ± 0 . 02 mm 2

2 . 22 ± 0 . 02 mm , π 1 . 23 ± 0 . 02 mm 2

2 . 22 ± 0 . 01 mm , π 1 . 23 ± 0 . 01 mm 2

2 . 14 ± 0 . 01 mm , π 1 . 14 ± 0 . 01 mm 2

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In the determination of Young's modulus $(Y = \frac{4 {ML}_{g}}{π ℓ d^{2}})$ by using Searle's method, a wire of length L = 2m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension $ℓ = 0.25$ mm in the length of the wire is observed. Quantities d and ℓ are measured using a screw gauge and micrometer, respectively. They have the same pitch of 0.5mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement

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Important Questions on Units and Measurements

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are

1 %, 2 %

and

3 %

respectively. The maximum percentage error in the detection of the dissipated heat will be:

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

Two parameters $a$ and $c$ are measured experimentally and used to determine a quantity $V$ given by $V =$ $\frac{\sqrt{3}}{2} a^{2} c$ . If the percentage errors in the measurement of $a$ and $c$ are respectively $1$ and $2$ , the percentage error in the measurement of $V$ is

HARD

Physics>Mechanics>Units and Measurements>Errors in Measurement

A physical quantity

y

is represented by the formula

y = m^{2} r^{- 4} g^{x} l^{- \frac{3}{2}}

If the percentage errors found in

y, m, r, l

and

g

are

18, 1, 0.5, 4

and

p

respectively, then find the value of

x

and

p

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

A physical quantity

P

is given as

P = \frac{a^{2} b^{3}}{c \sqrt{d}}

. The percentage error in the measurement of

a, b, c

and

d

are

1 %, 2 %, 3 %

and

4 %

respectively. The percentage error in the measurement of quantity

P

will be

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The power in an electrical circuit for a current of

5 \pm 0.4 A

and voltage

10 \pm 0.2 V

is measured at

10 %

error. To measure the power at

5 %

error the current should be measured at an error of

HARD

Physics>Mechanics>Units and Measurements>Errors in Measurement

Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 mm$ . The circular scale has $100$ divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.

Measurement condition	Main scale reading	Circular scale reading
Two arms of gauge touching each other without wire	$0$ division	$4$ divisions
Attempt- $1$ : With wire	$4$ divisions	$20$ divisions
Attempt- $2$ : With wire	$4$ divisions	$16$ divisions

What are the diameter and cross-sectional area of the wire measured using the screw gauge?

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The percentage errors of the measurements of two physical quantities $A$ and $B$ are given by

U_{A}

and

U_{B}

(U_{A} > U_{B})

. If the percentages errors of the measurements of

A^{2}, B^{2}, A B

are denoted by

U_{A^{2}}, U_{B^{2}}, U_{AB}

respectively, then

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The diameter and height of a cylinder are measured by a meter scale to be

12 .6 \pm 0 .1 cm

and

34 .2 \pm 0 .1 cm

, respectively. What will be the value of its volume in appropriate significant figures?

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

A physical quantity z depends on four observables

a, b, c

and

d

, as

z = \frac{a^{2} b^{\frac{2}{3}}}{\sqrt{c} d^{3}} .

The percentage of error in the measurement of

a, b, c

and

d

are

2 %, 1.5 %, 4 %

and

2.5 %

respectively. The percentage of error in

z

is :

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The density of the material of a cube can be estimated by measuring its mass and the length of one of its sides. If the maximum error in the measurement of mass and length are $0.3 %$ and $0.2 %$ respectively, the maximum error in the estimation of the density of the cube is approximately:

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The period of oscillation of a simple pendulum is

T = 2 π \sqrt{\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 wristwatch of

1 s

resolution. The accuracy in the determination of

g

HARD

Physics>Mechanics>Units and Measurements>Errors in Measurement

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is

δ T = 0.01 s

and he measures the depth of the well to be

L = 20

meters. Take the acceleration due to gravity

g = 10 m s^{- 2}

and the velocity of sound is

300 m s^{- 1}

. Then the fractional error in the measurement,

\frac{δ L}{L}

is closest to

HARD

Physics>Mechanics>Units and Measurements>Errors in Measurement

There are two vernier calipers both of which have $1 cm$ divided into $10$ equal divisions on the main scale. The Vernier scale of one of the calipers $(C_{1})$ has $10$ equal divisions that correspond to $9$ main scale divisions. The Vernier scale of the other caliper $(C_{2})$ has $10$ equal divisions that correspond to $11$ main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in $cm$ ) by calipers $C_{1}$ and $C_{2}$ respectively, are

Question Image

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

A torque meter is calibrated to reference standards of mass, length and time each with

5 %

accuracy. After calibration, the measured torque with this torque meter will have net accuracy of

HARD

Physics>Mechanics>Units and Measurements>Errors in Measurement

In an experiment to determine the acceleration due to gravity

g

, the formula used for the time period of a periodic motion is

T = 2 π \sqrt{\frac{7 (R - r)}{5 g}} .

The values of

R

and

r

are measured to be

(60 \pm 1) mm and (10 \pm 1) mm,

respectively. In five successive measurements, the time period is found to be

0.52 s

0.56 s

0.57 s

0.54 s

and

0.59 s

. The least count of the watch used for the measurement of time period is

0.01 s

. Which of the following statements (s) is (are) true?

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it ?

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

Diameter of a steel ball is measured using a Vernier calipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its Vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as:

S.No.	MS (cm)	VS divisions
1.	0.5	8
2.	0.5	4
3.	0.5	6

If the zero error is - 0.03 cm, then mean corrected diameter is:

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

A body accelerates from rest with a uniform acceleration

a

for a time

t .

The uncertainty in '

a

' is

8 %

and the uncertainty in '

t

' is

4 % .

The uncertainty in the speed is

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

In an experiment, the percentage of error occurred in the measurement of physical quantities

A, B, C

and

D

are 1%, 2%, 3% and 4%, respectively. Then the maximum percentage of error in the measurement

X

, where

X = \frac{A^{2} B^{\frac{1}{2}}}{C^{\frac{1}{3}} D^{3}}

will be

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be :

Important Questions on Units and Measurements

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