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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Find the number of significant figures in $3400$ .

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Important Questions on Units and Measurement

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

The number of significant figures in

0.07800

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

The distance of a circle is

2.486 m

. Its area with due regard to signifiant figures is (Given

π = 3.142

)

EASY

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

A body accelerates from rest with a uniform acceleration

a

for a time

t .

The uncertainty in '

a

' is

8 %

and the uncertainty in '

t

' is

4 % .

The uncertainty in the speed is

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?

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

For the four sets of three measured physical quantities as given below. Which of the following options is correct?

(i)

A_{1} = 24.36, B_{1} = 0.0724, C_{1} = 256.2

(i i)

A_{2} = 24.44, B_{2} = 16.082, C_{2} = 240.2

(i i i)

A_{3} = 25.2, B_{3} = 19.2812, C_{3} = 236.183

(i v)

A_{4} = 25, B_{4} = 236.191, C_{4} = 19.5

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

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

The area of a rectangular field (in

m^{2}

) of length

55.3 m

and breadth

25 m

after rounding off the value for correct significant digits 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:

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

Taking into account of the significant figures, what is the value of

9.99 m - 0.0099 m

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

The length and diameter of a cylinder are measured to be

10.1031 cm

and

2.0935 cm

respectively. The volume of the cylinder to an appropriate significant figures is

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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

In an experiment on a simple pendulum to determine the acceleration due to gravity, the student measures the length of the thread as

63.2 cm

and diameter of the pendulum bob as

2.256 cm .

The student should take the length of the pendulum to be

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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 ?

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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

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 ?

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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 °

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,

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

Order of magnitude of a physical quantity is the

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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 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?

Find the number of significant figures in 3400 .

Important Questions on Units and Measurement

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Find the number of significant figures in $3400$ .