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Q1. What are fundamental and derived units? Give some examples.

Solution

The units which can neither be derived from other units nor they can be further resolved into simpler units are called fundamental units. Examples: Mass, length etc. Those units which can be expressed in terms of the fundamental units are called derived units.  Example: speed, velocity, acceleration etc.

Q2. Define parsec and express it in metres?

Solution

One parsec is defined as the distance at which an arc of length one astronomical unit subtends an angle of one second of an arc . 1 parsec = 3.08 x 10¹⁶m.

Q3. What is meant by significant figures?

Solution

The significant figures refer to the number of important digits in a measured quantity which indicates confidence or precision with which scientist state a quantity.Significant figures are the digits whose values are accurately known in a particular measurement. Example: Suppose length of an object is 256.4 cm. It has four significant figures.

Q4. What do you mean by: (1) Systematic error (2) Least count errors

Solution

Systematic errors: The errors which tend to run in one direction either positive or negative are called systematic errors. These errors may be of the following type: (1) Instrumental error (2) Imperfection in experimental techniques (3) Personal errors (4) Error due to external causes.   Least count error: This error arises due to limitations imposed by the least count of measuring instrument. It is an uncertainty associated with the resolution of the measuring instrument.

Q5. What is one astronomical unit? Express it in metres?

Solution

Astronomical unit is the unit of length. It is the mean distance of the earth from the sun. 1 AU = 1.496 x 10¹¹ m.

Q6. Each side of a cube is measured to be 7.203m. What is the total surface area and volume of cube to appropriate significant figures?

Solution

It is given that the side of the cube is 7.203m. Therefore, number of significant figures in length is 4. Total surface area of cube, S = 6( area of one face) = 6l² = 6 (7.203)² S = (311.29925) m² By rounding off it to 4 significant figures, we get, S = 311.3 m² Volume of the cube, V = l³ = (7.203)³ = 373.714754427 m³ By rounding off it to 4 significant figures, we get, V = 373.7 m³

Q7. Under what conditions the zeros are not significant?

Solution

(i) When the first non-zero digit occurs after decimal, then all the zeros between decimal and first non zero digit are non significant. (ii) The zeros occuring on the extreme right in a whole number are not significant.

Q8. Name the unit used to measure the size of a nucleus and measure it in meters.

Solution

The unit used to measure the size of nucleus is Fermi. 1 Fermi = 10^-15 m.

Q9. State the number of significant figures in the following:

0.0005032 m²

2.64×10²⁴ kg

3.000 m

Solution

Significant figures in 0.0005032 m² are: 5, 0, 3, 2 The number of significant figures are 4 Significant figures in 2.64× 10²⁴ kg are: 2, 6, 4 The number of significant figures are 3 Significant figures in 3.000 are: 3,0,0,0 The number of significant figures are 4

Q10. Distinguish between the terms accuracy and precision.

Solution

Accuracy refers to the closeness of a measurement to the true value of the physical quantity. Precision refers to the resolution to which the quantity is measured. Precision is determined by the least count of the measuring instrument.