Units, Dimensions And Measurement Test

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Units, Dimensions And Measurement Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following quantities is unitless as well as dimensionless?

A
Angle

B
Solid angle

C
Mechanical equivalent of heat

D
Refractive index

Solution

In optics, the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as the ratio of the speed of light in vacuum relative to that in the considered medium.

This can be written mathematically as:

n = speed of light in a vacuum/speed of light in a medium

Since refractive index is the ratio of same quantities, so it has no unit and is a dimensionless quantity.
Question 2
1 / -0

Which of the following magnitudes is expressed most accurately?

A
1.3 x 10^-1 m

B
1.30 x 10^-2 m

C
1.3000 x 10^-4 m

D
1.3000 x 10^-6 m

Solution

The result is expressed in maximum number of significant figures in the 4^th option, so this option is the answer.
Question 3
1 / -0

In a screw gauge, if the zero mark on the head scale is below the index line of the pitch scale, then the error is

A
positive

B
negative

C
infinite

D
zero

Solution

In a screw gauge, if the zero mark on the head scale is below the index line of the pitch scale, then the error is positive and if zero mark on the head scale is above the line of pitch scale, then the error is negative.
Question 4
1 / -0

The length, breadth and thickness of a block are given as l = 12 cm, b = 6 cm and t = 2.45 cm, respectively. The volume of the block, according to the idea of significant figures, should be

A
1 × 10² cm³

B
2 × 10² cm³

C
1.763 × 10² cm³

D
1.83 × 10²cm³

Solution

Volume, V = l × b × t = 12 × 6 × 2.45

= 176.4 cm³

or V = 1.764 × 10² cm³

Since, the minimum number of significant figure is one in breadth, hence volume will also contain only one significant figure.

Hence, V = 2 × 10² cm³
Question 5
1 / -0

If a screw gauge moves 1 mm in two rotations, then the pitch of the screw gauge is

A
1.5 mm

B
2mm

C
0.5 mm

D
3 mm

Solution

Pitch = distance covered by screw head/number of rotations
= (1 mm)/2
= 0.5 mm
Question 6
1 / -0

How many significant figures are there in 0.000040009?

A
5

B
6

C
9

D
10

Solution

There are 5 significant figures in 0.000040009 because after the decimal, zeroes are counted only if they are between digits other than zero.

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Re-Attempt Weekly Quiz Competition

Units, Dimensions And Measurement Test - 3

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Units, Dimensions And Measurement Test - 3

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Question 1

Angle

Solid angle

Mechanical equivalent of heat

Refractive index

Solution

Question 2

1.3 x 10-1 m

1.30 x 10-2 m

1.3000 x 10-4 m

1.3000 x 10-6 m

Solution

Question 3

positive

negative

infinite

zero

Solution

Question 4

1 × 102 cm3

2 × 102 cm3

1.763 × 102 cm3

1.83 × 102 cm3

Solution

Question 5

1.5 mm

2mm

0.5 mm

3 mm

Solution

Question 6

5

6

9

10

Solution

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1.3 x 10^-1 m

1.30 x 10^-2 m

1.3000 x 10^-4 m

1.3000 x 10^-6 m

1 × 10² cm³

2 × 10² cm³

1.763 × 10² cm³

1.83 × 10²cm³