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QUESTION: 1

Dimensions cannot be used to ______.

Solution:

- 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 the Pure numbers since they are non-dimensional constants.and 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 which are dimensionally correct may or may not be accurately correct. Thus, Option Option (c). is correct answer for the Given question.
- Dimensional Equations are used for the conversions of the units thus this option can not be correct for the given question.

QUESTION: 2

Find the option with 3 significant figures.

Solution:

0.0268 have three significant figures where as 2.608 cm, 26.08 mm and 2.068 cm have four significant figures.

QUESTION: 3

Which of the following physical quantities has different dimensions?

Solution:

Dimension of work and energy are 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 are same i.e. [ML²T⁻²] but dimension of momentum is different ([MLT⁻¹]).

QUESTION: 4

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

Solution:

If radian correction is not considered in specific heat measurement. The measured value of specific heat will be. more than its actual value.

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 piece is:

Solution:

**► **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, required answer will be 2.4 g.

QUESTION: 6

What is the number of significant figures in 0.310×10^{3} ?

Solution:

Number of significant figures are 3, because 10^{3} is decimal multiplier.

QUESTION: 7

The number of significant figures in the distance of one light year , 9.4605 × 10^{15} m is:

Solution:

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

QUESTION: 8

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

Solution:

As the given number is itself written in the format of powers of ten, it is very obvious that all the non significant zeros are considered by the power of the and hence all the rest digits that are 3 in number are significant.

QUESTION: 9

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

Solution:

__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.

QUESTION: 10

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

Solution:

- 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.

QUESTION: 11

Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv^{3}, where K is a constant. The dimensions of K are:

Solution:

QUESTION: 12

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

Solution:

- 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.

QUESTION: 13

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

Solution:

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

QUESTION: 14

Which of the quantity is dimensionless?

Solution:

Among all the given quantities, work, force and area can be expressed as products of some quantities which have non zero dimension, but angle is defined as the ratio of arc length to radius which is hence dimensionless.

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?

Solution:

The more significant numbers in measurement the more correct it is.

QUESTION: 16

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

Solution:

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.

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:

Solution:

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

QUESTION: 18

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

Solution:

**► **Pressure = Force/Area = ML^{1}T^{-2}/ L^{2} = [M L^{-1} T^{-2}]

**► **Stress = Force/Area = ML^{1}T^{-2}/ L^{2} = [ML^{-1}T^{-2}]

**► **Coefficient of elasticity = Stress/Strain = [ML^{-1}T^{-2}]

QUESTION: 19

Find the option with 5 significant figures:

Solution:

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

In **option d, **the number has 5 significant figures.

QUESTION: 20

A dimensionless quantity ______.

Solution:

- A dimensionless quantity has no dimensions but it may or may not have units.
- Two very common examples of dimensionless quantities are refractive index which does not have any units and angle which has units (degrees, radians).

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