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.

EASY

Earn 100

Give an example of an inappropriate device used for measurement and causing error.

Important Questions on Measurement of Physical Quantities

MEDIUM

Science>Physics>Measurement of Physical Quantities>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 °

EASY

Science>Physics>Measurement of Physical Quantities>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

Science>Physics>Measurement of Physical Quantities>Errors in Measurement

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

EASY

Science>Physics>Measurement of Physical Quantities>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

Science>Physics>Measurement of Physical Quantities>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

Science>Physics>Measurement of Physical Quantities>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)?

MEDIUM

Science>Physics>Measurement of Physical Quantities>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 ______.

HARD

Science>Physics>Measurement of Physical Quantities>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)

EASY

Science>Physics>Measurement of Physical Quantities>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

Science>Physics>Measurement of Physical Quantities>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

-

MEDIUM

Science>Physics>Measurement of Physical Quantities>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

Science>Physics>Measurement of Physical Quantities>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

Science>Physics>Measurement of Physical Quantities>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

Science>Physics>Measurement of Physical Quantities>Errors in Measurement

There are atomic clocks capable of measuring time with an accuracy of

1

part in

10^{11}

. If two such clocks are operated with precision, then after running for

5000

years, these will record

HARD

Science>Physics>Measurement of Physical Quantities>Errors in Measurement

The focal length of a mirror is given by

\frac{2}{f} = \frac{1}{v} - \frac{1}{u}

. If in the measurement of

u

and

v

, the errors are equal to

p

each, then the relative error in

f

EASY

Science>Physics>Measurement of Physical Quantities>Errors in Measurement

While measuring the length of an object it was observed that the zero of the vernier lies between

1.4

and

1.5

of the main scale and the fifth vernier division coincides with the

9 - 0

main scale division. If the length of the object measured is

l

, then the value of

(l - 1.4)

in terms of the least count

C

of the instrument is

MEDIUM

Science>Physics>Measurement of Physical Quantities>Errors in Measurement

The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are

4 %

and

3 %

respectively, the maximum error in the measurement of density will be

EASY

Science>Physics>Measurement of Physical Quantities>Errors in Measurement

Calculate the fractional error

(\frac{Δ x}{x}),

x = a^{n}

MEDIUM

Science>Physics>Measurement of Physical Quantities>Errors in Measurement

R = 65 \pm 1 Ω, l = 5 \pm 0.1 m m

and

d = 10 \pm 0.5 m m .

Find error in calculation of resistivity.

EASY

Science>Physics>Measurement of Physical Quantities>Errors in Measurement

Calculate the fractional error

(\frac{Δ x}{x}),

x = a^{n}

Give an example of an inappropriate device used for measurement and causing error.

Important Questions on Measurement of Physical Quantities

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