HARD

Earn 100

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?

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Important Questions on Physical World and Measurement

MEDIUM

Physics>General Physics>Physical World and Measurement>Error Analysis

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:

EASY

Physics>General Physics>Physical World and Measurement>Error Analysis

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>General Physics>Physical World and Measurement>Error Analysis

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>General Physics>Physical World and Measurement>Error Analysis

In a simple pendulum experiment for determination of acceleration due to gravity

(g)

, time taken for

20

oscillations is measures by using a watch of

1

second least count. The mean value of time taken comes out to be

30 s

. The length of the pendulum is measured by using a meter scale of least count

1 m m

and the value obtained is

55.0 c m

. The percentage error in the determination of

g

is close to

MEDIUM

Physics>General Physics>Physical World and Measurement>Error Analysis

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>General Physics>Physical World and Measurement>Error Analysis

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>General Physics>Physical World and Measurement>Error Analysis

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>General Physics>Physical World and Measurement>Error Analysis

Using screw gauge of pitch

0.1 cm

and

50

divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as,

EASY

Physics>General Physics>Physical World and Measurement>Error Analysis

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

Physics>General Physics>Physical World and Measurement>Error Analysis

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>General Physics>Physical World and Measurement>Error Analysis

In the density measurement of a cube, the mass and edge length are measured as

(10.00 \pm 0.10) k g

and

(0.10 \pm 0.01) m,

respectively. The error in the measurement of density is:

MEDIUM

Physics>General Physics>Physical World and Measurement>Error Analysis

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:

EASY

Physics>General Physics>Physical World and Measurement>Error Analysis

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>General Physics>Physical World and Measurement>Error Analysis

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>General Physics>Physical World and Measurement>Error Analysis

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

EASY

Physics>General Physics>Physical World and Measurement>Error Analysis

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 :

EASY

Physics>General Physics>Physical World and Measurement>Error Analysis

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>General Physics>Physical World and Measurement>Error Analysis

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>General Physics>Physical World and Measurement>Error Analysis

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

)

HARD

Physics>General Physics>Physical World and Measurement>Error Analysis

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 ?

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

Important Questions on Physical World and Measurement

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