Zero error is defined as the condition where a measuring instrument records a reading when no reading is required. If on bringing the flat end of the screw in contact with the stud, the zero mark of the circular scale coincides with the zero mark on the baseline of the main scale, the instrument is said to be free from zero error. In case of Vernier calipers it occurs when a zero on the main scale does not coincide with a zero on Vernier scale it is called zero error for Vernier.

Using the expression 2 d sin θ = λ , one calculates the values of d by measuring the corresponding angle θ in the range 0 to 90 ° . The wavelength λ is exactly known and the error in θ is constant for all the values of θ . As θ increases from 0 °

The fractional error in d decreases.

The absolute error in d remains constant.

The absolute error in d increases.

The fractional error in d remains constant.

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What is zero error?

Important Questions on Units and Measurements

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

The relative error in the determination of the surface area of a sphere is

α

. The relative error in the determination of its volume is

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

The radius of a sphere is measured to be

(7.50 \pm 0.85) cm

. Suppose the percentage error in its volume is

x

. The value of

x

, to the nearest

x

, is ___ .

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are:

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

The period of oscillation of a simple pendulum is given by

T = 2 π \sqrt{\frac{L}{g}}

, where

L

is the length of the pendulum and

g

is the acceleration due to gravity. The length is measured using a meter scale which has

500

divisions. If the measured value

L

50 cm

, the accuracy in the determination of

g

1.1 %

and the time taken for

100

oscillations is

100

seconds, what should be the possible error in measurement of the clock in one minute (in milliseconds)?

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

A simple pendulum is being used to determine the value of gravitational acceleration

g

at a certain place. The length of the pendulum is

25.0 c m

and a stopwatch with

1 s

resolution measures the time taken for

40

oscillations to be

50 s

. The accuracy in

g

is:

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 ?

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Physics>Mechanics>Units and Measurements>Errors in Measurement

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at

40 cm

from the pole of the mirror is formed at distance

120 cm

from the pole of the mirror. These distances are measured with a modified scale in which there are

20

small divisions in

1 cm

. The value of error in measurement of focal length of the mirror is

\frac{1}{K} cm

. The value of

K

is ______.

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Physics>Mechanics>Units and Measurements>Errors in Measurement

The length of an object is measured using a vernier system whose main scale is

30 cm

long with

600

divisions. If

19

divisions of the main scale coincide with

20

divisions of the vernier scale, then its least count is

EASY

Physics>Mechanics>Units and Measurements>Errors in Measurement

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings

5.50 mm

5.55 mm

5.34 mm

5.65 mm

. The average of these four reading is

5.5375 mm

and the standard deviation of the data is

0.07395 mm

. The average diameter of the pencil should therefore be recorded as :

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is

(\frac{x}{100}) % .

If the relative errors in measuring the mass and the diameter are

6.0 %

and

1.5 %

respectively, the value of

x

-

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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:

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Physics>Mechanics>Units and Measurements>Errors in Measurement

The density of a material, in the shape of a cube, is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are

1.5 %

and

1 %

, respectively, the maximum error in determining the density is:

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

Using the expression

2 d \sin θ = λ

, one calculates the values of

d

by measuring the corresponding angle

θ

in the range

0

90 °

. The wavelength

λ

is exactly known and the error in

θ

is constant for all the values of

θ

. As

θ

increases from

0 °

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 $P$ is described by the relation $P = a^{\frac{1}{2}} b^{2} c^{3} d^{- 4}$ . If the relative errors in the measurement of $a$ , $b$ , $c$ and $d$ respectively, are $2 %$ , $1 %$ , $3 %$ and $5 %$ . Then the relative error in $P$ will be:

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

HARD

Physics>Mechanics>Units and Measurements>Errors in Measurement

Students

A, B

and

C

measure the length of a room using

25 m

long measuring tape of least count

LC

0.5 cm,

meter-scale of

LC 0.1 cm

and a foot-scale of

LC 0.05 cm,

respectively. If the specified length of the room is

9.5 m,

then which of the following students will report the lowest relative error in the measured length?

(1 foot = 30.48 cm)

MEDIUM

Physics>Mechanics>Units and Measurements>Errors in Measurement

A student measures the time period of

100

oscillations of a simple pendulum four times. The data set is

90 s

91 s

95 s

and

92 s

. If the minimum division in the measuring clock is

1 s

, then the reported mean time should be:

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.

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The statement which is most likely to be correct?

What is zero error?

Important Questions on Units and Measurements

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