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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According to significant figure convention the result obtained by adding 12.11, 18.0 and 1.012 is

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Important Questions on Units and Measurement

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Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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:

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Physics>Mechanics>Units and Measurement>Precision and Significant Figures

The period of oscillation of a simple pendulum is

T = 2 π \sqrt{\frac{l}{g}} .

Measured value of

l

20.0 cm

, known to

1 mm

accuracy and time for

100

oscillations of the pendulum is found to be

90 s

using a wristwatch of

1 s

resolution. The accuracy in the determination of

g

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Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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 °

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Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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 Measurement>Precision and Significant Figures

Diameter of a steel ball is measured using a Vernier calipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its Vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as:

S.No.	MS (cm)	VS divisions
1.	0.5	8
2.	0.5	4
3.	0.5	6

If the zero error is - 0.03 cm, then mean corrected diameter is:

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Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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:

HARD

Physics>Mechanics>Units and Measurement>Precision and Significant Figures

The diameter of a cylinder is measured using a vernier callipers with no zero error. It is found that the zero of the vernier scale lies between

5.10 cm

and

5.15 cm

of the main scale. The vernier scale has

50

divisions equivalent to

2.45 cm

. The

24^{th}

division of the vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is,

EASY

Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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:

EASY

Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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 Measurement>Precision and Significant Figures

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 ?

HARD

Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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>Units and Measurement>Precision and Significant Figures

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?

EASY

Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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 Measurement>Precision and Significant Figures

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 :

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Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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

EASY

Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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:

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Physics>Mechanics>Units and Measurement>Precision and Significant Figures

The area of a square is

5.29 c m^{2} .

The area of

7

such squares taking into account the significant figures is:

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Physics>Mechanics>Units and Measurement>Precision and Significant Figures

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 Measurement>Precision and Significant Figures

The diameter and height of a cylinder are measured by a meter scale to be

12 .6 \pm 0 .1 cm

and

34 .2 \pm 0 .1 cm

, respectively. What will be the value of its volume in appropriate significant figures?

HARD

Physics>Mechanics>Units and Measurement>Precision and Significant Figures

There are two vernier calipers both of which have $1 cm$ divided into $10$ equal divisions on the main scale. The Vernier scale of one of the calipers $(C_{1})$ has $10$ equal divisions that correspond to $9$ main scale divisions. The Vernier scale of the other caliper $(C_{2})$ has $10$ equal divisions that correspond to $11$ main scale divisions. The readings of the two calipers are shown in the figure. The measured values (in $cm$ ) by calipers $C_{1}$ and $C_{2}$ respectively, are

Question Image

According to significant figure convention the result obtained by adding 12.11, 18.0 and 1.012 is

Important Questions on Units and Measurement

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