Section B CRQ's

 

Section B 

                CRQ's

1. Give an example of (1) a physical quantity which has a unit but no dimensions. (II) a physical quantity which has neither unit not dimensions. (III) a constant which has a unit. (IV) a constant which has no unit.

Ans..

I. Physical quantity with a unit but no dimensions: Planar angle in radians. It's a unit of angle measurement and doesn't have any dimensions.

II. Physical quantity with neither unit nor dimensions: Pure number, like the coefficient in a dimensionless quantity such as the coefficient of friction or the fine-structure constant in physics.

III. Constant with a unit: Avogadro's number (6.022 x 10^23 mol^-1) is a constant with the unit "per mole."

IV. Constant with no unit: The mathematical constant π (pi) doesn't have any physical unit associated with it.

2. When rounding the product or quotient of two measurements, is it necessary to consider Significant digit ?

Ans..  Yes, when rounding the product or quotient of two measurements, it's important to consider significant digits. The result should be rounded to the same number of significant digits as the measurement with the fewest significant digits. This helps maintain the accuracy and precision of the calculated value and ensures that the final result reflects the limitations of the original measurements.

5. You measure the radius of a wheel to be 4.16 cm. If you multiply by 2 to get diameter, should you write the result as 8 cm or as 8.32 cm? Justify your answer.

Ans

Formula for the relation between the radius and diameter of a circle

Given Data:

The radius of the wheel (R) is 4.16 cm

The diameter is a line segment that passes through the center of a circle and touches the circumference of the circle with its endpoints.

The formula for the diameter of a wheel is

D= 2R...... (I)

Calculating the radius of the wheel

To find the diameter, take the value of radius in equation (i).

Thus, you have

D= 2 × 4.16D = 8.32 cm

The calculated value of the diameter is 8.32 cm.

The value of radius 4.16 cm has three significant digits. By the rules of significant digits, the diameter must also have three significant digits.

The value 8 cm has only one significant digit. In comparison, 8.32 cm has three significant digits, equal to those in 4.16 cm. Therefore, 8.32 cm is the more accurate value of the diameter.

6. If y=a+bt+ct where y is in meters and t in seconds, what is the unit of c?

Solution

Dimension of a,bt,ct2 should be equal to x

x=[L]

So, the dimension of bt will be equal to that of 'x'

b t=[L]

b=[T][L]

b=[LT−1]

The dimension of c can be obtained as:

ct2=[L]

c=[T2][L]

c=[LT−2]

7. Differentiate between accuracy and precision

Ans...

8. Define dependent and independent variables

Ans...

A1. Dependent variable: 

                        A variable that is being measured or observed in an experiment or study, and is expected to change as a result of the manipulation of the independent variable.

Independent variable: A variable that is manipulated in an experiment or study to observe the effect it has on a dependent variable. It's also referred to as the predictor variable, explanatory variable, or input variable.

9. Differentiate systematic error and random error.

Ans...

11. Describe least count of Vernier and screw gauge micrometer.

The least count of a measuring instrument is the smallest measurement that can be accurately recorded by that instrument.

In a Vernier caliper, the least count is the difference between one main scale division and one Vernier scale division. It helps in obtaining more precise measurements by reading both scales.

For a screw gauge micrometer, the least count is determined by the pitch of the screw and the number of divisions on the circular scale. It's the smallest distance the screw can move, which corresponds to one division on the circular scale.

The formulas to calculate the least count are:

- For Vernier caliper: Least Count = Value of one main scale division - Value of one Vernier scale division.

- For screw gauge micrometer : Least Count = Pitch of screw / Number of divisions on the circular scale.

These least counts contribute to the precision of measurements made using these instruments.

12... Describe extrapolation methods

 Extrapolation: Estimating Beyond Observed Data:

Extrapolation is a statistical technique involving the estimation of values beyond the scope of collected data. It entails predicting future or unobserved data by identifying trends or patterns in existing data.

Method of Extrapolation: Projecting Trends

Extrapolation involves extending known trends or patterns from existing data to make predictions about unseen data. For instance, consider a volume-temperature graph where extending a line until it intersects the temperature axis predicts a zero Kelvin temperature.

Key Concept: Using Existing Patterns

The core idea of extrapolation is utilizing established data patterns to anticipate outcomes that lie beyond the range of available data.

Summary: Predicting Unseen Data

In summary, extrapolation is a valuable statistical tool to make educated guesses about future or unobserved data based on patterns identified within existing data.