Match the physical quantities with their correct SI units. List-I List-II (A) Planck's constant (I) kg m s - 2 (B) Torque (II) kg - 1 m 3 (C) Weight (III) m 2 kg s - 1 (D) Specific volume (IV) kg m 2 s - 2 The correct match is

A = III , B = IV , C = I , D = II

A = II , B = IV , C = I , D = III

A = IV , B = I , C = II , D = III

A = II , B = III , C = I , D = IV

Velocity v and acceleration a in two systems of units 1 and 2 are related as v 2 = n m 2 v 1 and a 2 = a 1 m n respectively. Here m and n are constants. The relations for distance and time in two systems respectively are

n 3 m 3 L 1 = L 2 and n 2 m T 1 = T 2

L 1 = n 4 m 2 L 2 and T 1 = n 2 m T 2

L 1 = n 2 m L 2 and T 1 = n 4 m 2 T 2

n 2 m L 1 = L 2 and n 4 m 2 T 1 = T 2

MEDIUM

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The least count of a measuring scale is $1 mm$ . The heights two students is measured with it. What will be the error in the difference between their heights?

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Important Questions on Units and Measurements

MEDIUM

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

A huge circular arc of length $4.4 ly$ subtends an angle $4 s$ at the centre of the circle. How long it would take for a body to complete $4$ revolution if its speed is $8 AU$ per second?
Given : $1 ly = 9.46 \times 10^{15} m$

$1 AU = 1.5 \times 10^{11} m$

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

A spherometer has

20

threads per

cm

. Its circular scale has

100

divisions. The least count of the sphere is

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

If $E$ and $H$ represents the intensity of electric field and magnetizing field respectively, then the unit of $\frac{E}{H}$ will be:

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

A student measured the diameter of a small steel ball using a screw gauge of least count

0.001 cm .

The main scale reading is

5 mm

and zero division of the circular scale coincides with

25

divisions above the reference level. If the screw gauge has a zero error of

- 0.004 cm .

the correct diameter of the ball is__________

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

The dimension of light year

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

Match the following?

Column -I		Column -II
(a)	Conductance	(i)	Gray
(b)	Magnetic Induction	(ii)	Lumen
(c)	Absorbed dose	(iii)	Tesla
(d)	Luminous flux	(iv)	Siemens

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

An accurate measurement implies that

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

Plane angle and solid angle have:

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

Match the physical quantities with their correct $SI$ units.

	List-I		List-II
(A)	Planck's constant	(I)	$kg m s^{- 2}$
(B)	Torque	(II)	${kg}^{- 1} m^{3}$
(C)	Weight	(III)	$m^{2} kg s^{- 1}$
(D)	Specific volume	(IV)	$kg m^{2} s^{- 2}$

The correct match is

HARD

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

A person in front of a mountain is beating a drum at the rate of

40

per minute and hears no distinct echo. If the person moves

90 m

closer to the mountain, he has to beat the drum at

60

per minute to not hear any distinct echo. The speed of sound is

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

The commutator bracket

[X Y, Z]

is expanded as

MEDIUM

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

The angular diameter of a planet measured from earth is

90 " .

If the diameter of the planet is

π \times 10^{6} m,

then its distance from the earth is

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

The distance of the Sun from earth is

1.5 \times 10^{11} m

and its angular diameter is

2000''

when observed from the earth. The diameter of the Sun will be

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

The angular speed of a fly-wheel making

180 rpm

is ________

MEDIUM

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

Velocity

(v)

and acceleration

(a)

in two systems of units

1

and

2

are related as

v_{2} = \frac{n}{m^{2}} v_{1}

and

a_{2} = \frac{a_{1}}{m n}

respectively. Here

m

and

n

are constants. The relations for distance and time in two systems respectively are

HARD

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

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?

HARD

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

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

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

The nearest star to our solar system is

4.3

light years away. The distance of this star in Parsec is (Mean distance between the earth and the sun

= 1.5 \times 10^{11} m

and one light year

= 9.46 \times 10^{15} m)

EASY

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

The angle of

1'

(minute of arc) in radian is nearly equal to

MEDIUM

Physics>Mechanics>Units and Measurements>Accuracy and Precision of Instruments

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

The least count of a measuring scale is 1 mm. The heights two students is measured with it. What will be the error in the difference between their heights?

Important Questions on Units and Measurements

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The least count of a measuring scale is $1 mm$ . The heights two students is measured with it. What will be the error in the difference between their heights?