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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How do you calculate standard error?

Important Questions on Physical World and Measurement

EASY

Physics>Mechanics>Physical World and Measurement>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>Physical World and Measurement>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>Physical World and Measurement>Errors in Measurement

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

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Physics>Mechanics>Physical World and Measurement>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>Physical World and Measurement>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:

HARD

Physics>Mechanics>Physical World and Measurement>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?

MEDIUM

Physics>Mechanics>Physical World and Measurement>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 ______.

EASY

Physics>Mechanics>Physical World and Measurement>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 :

EASY

Physics>Mechanics>Physical World and Measurement>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>Physical World and Measurement>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

-

HARD

Physics>Mechanics>Physical World and Measurement>Errors in Measurement

The current voltage relation of diode is given by I = (e¹⁰⁰⁰^V/T - 1) mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring

\pm 0.01 V

while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ?

MEDIUM

Physics>Mechanics>Physical World and Measurement>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>Physical World and Measurement>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>Physical World and Measurement>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

Physics>Mechanics>Physical World and Measurement>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:

EASY

Physics>Mechanics>Physical World and Measurement>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

HARD

Physics>Mechanics>Physical World and Measurement>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>Physical World and Measurement>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>Physical World and Measurement>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>Physical World and Measurement>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?

How do you calculate standard error?

Important Questions on Physical World and Measurement

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