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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The length of a massless rod is measured using vernier callipers having $10$ vernier scale divisions and least count of $0.1 mm$ . Two masses $1.00 \pm 0.01 kg$ and $4.00 \pm 0.02 kg$ are attached to its ends. If reading of vernier scale is $5$ divisions coinciding with $1.3 cm$ , what is the $%$ error in locating centre of mass from lighter mass?

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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

In an experiment, the mass of an object is measured by applying a known force on it, and then measuring its acceleration. If in the experiment, the measured values of applied force and the measured acceleration are

F = (10.0 \pm 0.2) N

and

a = (1.00 \pm 0.01) m s^{- 2},

respectively, the mass of the object is

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:

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 ?

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

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The percentage errors in quantities

P

Q

R

and

S

are

0.5 %

1 %

3 %

and

1.5 %

respectively in the measurement of a physical quantity

A= \frac{P^{3} Q^{2}}{\sqrt{R} S}

. The maximum percentage error in the value of

A

will be:

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

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

If one takes into account the finite mass of the proton, the correction to the binding energy of the hydrogen atom is approximately (mass of proton

= 1 .60 \times 10^{- 27} kg,

mass of an electron

= 9 .10 \times 10^{- 31} kg

)

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The length and width of a rectangular room are measured to be

(3 .95 \pm 0 .05) m

and

(3 .05 \pm 0 .05) m

, respectively, the area of the floor is

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

Two students $P$ and $Q$ perform an experiment to verify Ohm's law for a conductor with resistance $R$ . They use a current source and a voltmeter with the least counts of $0.1 mA$ and $0.1 mV$ , respectively. The plots of the variation of voltage drop $V$ across $R$ with current $I$ for both are shown below.

Question Image

The statement which is most likely to be correct?

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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