Test: Significant Figures & Dimensions

• 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. 

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. 

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]).

S_P​(Heat) = mcΔt

If radian correction is not considered then Δt will increase.

So, S_P​ will also increase.

Hence option 'A' is correct.

 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.

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. 

As the power of 10 is irrelevant in the determination of significant figures hence, the numbers of significant figures are 5 i.e. 9,4,6,0,5

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).

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. 

• 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. 

• 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. 

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

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.

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

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. 

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

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. 

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

In option d, the number has 5 significant figures.

• 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.