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Test: Significant Figures & Dimensions


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Test: Significant Figures & Dimensions - Question 1

Dimensions cannot be used to ______.

Detailed Solution for Test: Significant Figures & Dimensions - Question 1
  • Dimensional Equations are used to derive the Relations between the Physical quantities.
  • Also, they are used to check the correctness of the Equation by the Principle of the homogeneity of the dimensions.

Hence, Option (a) and option (b) are true for the Dimensional equation. Thus, It is not correct for the given questions.

  • Dimensional Equations are not valid for Pure numbers since they are non-dimensional constants. Also, they do not provide the value of the Constant of the Proportionality.
  • Thus, we can also say that all equations which are correct must be dimensionally correct but all those equations that are dimensionally correct may or may not be accurately correct. Thus, Option (c) is the correct answer for the given question.
  • Dimensional Equations are used for the conversions of the units thus (d) option can not be correct for the given question.

Hence, option C is the correct answer as it is an incorrect statement. 

Test: Significant Figures & Dimensions - Question 2

Find the option with 3 significant figures.

Detailed Solution for Test: Significant Figures & Dimensions - Question 2

The significant figures in any number are all certain digits plus one doubtful digit. Certain rules are followed which are as under:

1) All one zero digits in a number are significant.

2) The zeroes between two non-zero digits are always significant.

3) The zeros written to the left of the first non-zero digit in a number are non-significant. They simply indicate the position of the decimal point.

4) All zeros placed to the right of a decimal point in a number are significant.

Since, 0.0268 has three significant figures whereas 2.608 cm, 26.08 mm and 2.068 cm have four significant figures, A is the correct answer. 

Test: Significant Figures & Dimensions - Question 3

Which of the following physical quantities has different dimensions?

Detailed Solution for Test: Significant Figures & Dimensions - Question 3

Dimension of work and energy are the same i.e. [ML²T⁻²].
 Power = Energy/Time,
 Energy = Power × Time (in terms of hour instead of second),
 Energy = Watt × Hour,
= [ML²T⁻³] [T],
= [ML²T⁻²].
But, Momentum(p) = Mass × Velocity,
 p = [M] [LT⁻¹],
 p = [MLT⁻¹].
Hence the Dimension of work, energy and watt-hour is the same i.e. [ML²T⁻²] but the dimension of momentum is different ([MLT⁻¹]).

Test: Significant Figures & Dimensions - Question 4

If radian correction is not considered in specific heat measurement. The measured value of specific heat will be ______.

Detailed Solution for Test: Significant Figures & Dimensions - Question 4

SP​(Heat) = mcΔt

If radian correction is not considered then Δt will increase.

So, SP​ will also increase.

Hence option 'A' is correct.

Test: Significant Figures & Dimensions - Question 5

Two gold pieces, each of mass 0.035g, are placed in a box of mass 2.3 g. The total mass of the box with gold pieces is:

Detailed Solution for Test: Significant Figures & Dimensions - Question 5

 Mass of Gold pieces = 2 × 0.035 = 0.070 g
 Mass of box = 2.3 g
 Total mass of box with gold pieces = 0.070 + 2.3 = 2.370 g

Since the answer should be in 2 significant digits, therefore, on rounding off, we get 2.4 g.

Thus, the required answer will be 2.4 g.

Test: Significant Figures & Dimensions - Question 6

 What is the number of significant figures in 0.310×103 ?

Detailed Solution for Test: Significant Figures & Dimensions - Question 6

The number of significant figures is 3 because 103 is a decimal multiplier.

So. after calculating this number, we will get 0310 which is also a 3 significant figure number. 

Test: Significant Figures & Dimensions - Question 7

The number of significant figures in the distance of one light year , 9.4605 × 1015 m is:

Detailed Solution for Test: Significant Figures & Dimensions - Question 7

As the power of 10 is irrelevant in the determination of significant figures hence, the numbers of significant figures are 5.

Test: Significant Figures & Dimensions - Question 8

The numbers of significant figures in 1.84 x10-27 kg are:

Detailed Solution for Test: Significant Figures & Dimensions - Question 8

As the power of 10 is irrelevant to the determination of significant figures hence, the numbers of significant figures are 3 (1, 8 and 4).

Test: Significant Figures & Dimensions - Question 9

The multiplication of 10.610 with 0.210 upto correct number of significant figure is:

Detailed Solution for Test: Significant Figures & Dimensions - Question 9

The multiplication of the numbers:
10.610 × 0.210 = 2.2281

Since, the numbers 10.610 and 0.210 have 5 and 3 significant digits, respectively. So, the final result must also have 3 significant digits.

The final answer is 2.23 after rounding off 2.2281. 

Test: Significant Figures & Dimensions - Question 10

Numbers of significant figures in the volume of a cube of side 6.103 m are:

Detailed Solution for Test: Significant Figures & Dimensions - Question 10
  • As per rule, zero between two non zero digits are significant.
  • The number of a significant figure in the length of the side is 4.
  • So the calculated volume should be rounded off to 4 significant figures. Multiplying numbers do not increase significant figures.

Therefore, the correct answer is 4. 

Test: Significant Figures & Dimensions - Question 11

Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv3, where K is a constant. The dimensions of K are:

Detailed Solution for Test: Significant Figures & Dimensions - Question 11

Test: Significant Figures & Dimensions - Question 12

The order of magnitude of a number expressed in scientific notation is ______.

Detailed Solution for Test: Significant Figures & Dimensions - Question 12
  • Scientific notation is the method of writing, or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10. 
  • To convert a regular number to scientific notation, we first rewrite it as a decimal, then multiply it by a power of 10.
  • There is an infinite number of ways to do this for any given number, but we always prefer the one that has only a single digit in front of the decimal point. 
Test: Significant Figures & Dimensions - Question 13

The numbers of significant figures in 9.1 x10-31 kg are:

Detailed Solution for Test: Significant Figures & Dimensions - Question 13

As the power of 10 is irrelevant to the determination of significant figures hence, the numbers of significant figures are 2 (9 and 1).

Test: Significant Figures & Dimensions - Question 14

Which of the quantity is dimensionless?

Detailed Solution for Test: Significant Figures & Dimensions - Question 14

Among all the given quantities, work, force and area can be expressed as products of some quantities which have non-zero dimensions, but the angle is defined as the ratio of arc length to the radius which is dimensionless because both arc length and radius have the same dimensions which when taken a ratio of, will get cancelled out. 

Additional Information: A dimensionless quantity is the one for which no physical dimension is assigned. It is also known as a bare, pure, or scalar quantity or also as a quantity of dimension one.

Test: Significant Figures & Dimensions - Question 15

Three students measured length of a needle with meter rod and recorded as :
(i) 0.2145m
(ii) 0.21m
(iii) 0.214m
Which one is correct record?

Detailed Solution for Test: Significant Figures & Dimensions - Question 15

 

the correct answer should be C because a meter rod can only read upto two decimal points

Test: Significant Figures & Dimensions - Question 16

After a decimal point, the number is less than 5 which is to be neglected, then retained number:

Detailed Solution for Test: Significant Figures & Dimensions - Question 16

In rounding off numbers, the last figure kept should be unchanged if the first figure dropped is less than 5.
Example: If only one decimal is to be kept, then 6.422 becomes 6.4.

Hence the correct answer is C. 

Test: Significant Figures & Dimensions - Question 17

Mary bought a tank whose dimensions are 5.6cm, 8.2cm and 12.8 cm. The volume of water (in cm³) that can be stored in tank (correct up to four significant figures) is:

Detailed Solution for Test: Significant Figures & Dimensions - Question 17

Volume of water = Volume of the tank = Length * breadth * height = 5.6 * 8.2 * 12.8 = 587.776

Volume, correct up to 4 significant figure = 587.8

Test: Significant Figures & Dimensions - Question 18

Three physical quantity having dimensions [ML-1T-2] are:

Detailed Solution for Test: Significant Figures & Dimensions - Question 18

Pressure = Force/Area = ML1T-2/ L2 = [M L-1 T-2]
Stress = Force/Area   = ML1T-2/ L2 = [ML-1T-2]
Coefficient of elasticity = Stress/Strain = [ML-1T-2]

Hence, the correct answer is C. 

Test: Significant Figures & Dimensions - Question 19

Find the option with 5 significant figures:

Detailed Solution for Test: Significant Figures & Dimensions - Question 19

In option a, b and c, we only have 4 significant figures in the number

In option d, the number has 5 significant figures.

Test: Significant Figures & Dimensions - Question 20

A dimensionless quantity ______.

Detailed Solution for Test: Significant Figures & Dimensions - Question 20
  • Dimensionless quantities are the quantities that do not possess any dimensions.
  • An example of such a quantity is specific gravity (ratio of absolute density of an object to absolute density of water).
  • As these quantities are often a pure ratio between similar physical quantities they do not possess dimension and hence no units. 
  • But when we look at the dimensionless quantity- angle, it has a unit assigned to it, the radians or degrees.
  • So we cannot say that all dimensionless quantities are unitless.

Therefore, the correct answer is D. 

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