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**Q.1. What is the necessity of selecting some units as fundamental units****Ans.** The number of physical units required to be measured is very large. If a separate unit is defined for each of them, then it will become very difficult to remember all of them as they will be quite unrelated to each other.**Q.2. How is SI a coherent system of units?****Ans.** In SI, all derived units can be obtained by multiplying and dividing the basic and supplementary units and no numerical factors are required to be introduced. So SI is a coherent system of units.**Q.3. In defining the standard of length, (the prototype metre), we have to specify the temperature at which the measurement should be made. Are we justified in calling length a fundamental quantity, if another physical quantity (temperature) has to be specified in choosing a standard?****Ans.** Yes, the choice of length as a fundamental quantity is justified. The modem definition of metre in terms of wavelength of light radiation is not affected by temperature.**Q.4. Do Å and AU stand for the same unit of length?****Ans. **No. 1 Å (angstrom) =10^{-10} m 1 AU (astronomical unit) = 1.496 × 10^{11} m.**Q.5. Why is it convenient to express the distances of stars in terms of light year rather than in metre or kilometre?****Ans. **One light year = 9.46 × 10^{15} m = 9.46 × 10^{12} km. As the distances of stars are extra-ordinarily large, so it is convenient to express them in light year rather than in metre or kilometre.**Q.6. Comment on the statement: "To define a physical quantity for which no method of measurement is given or known has no meaning."****Ans. **The given statement is not correct. A physical quantity, if it is called so, must have a physical meaning. If it cannot be measured by any direct method, these must be some indirect method for its measurement. Entropy is one such physical quantity.**Q.7. Is the measure of an angle dependent upon the unit of length?****Ans. **

θ(radian) = (Arc/Radius)

As an angle is the ratio of the length of an arc and the radius i.e., it is the ratio of two lengths, so the measure of an angle does not depend upon the unit of length.**Q.8. What is meant by angular diameter of the moon? What is its value****Ans.** The angle subtended by the two diametrically opposite ends of the moon at a point on the earth is called angular diameter of the moon. Its value is about 0.5∘.**Q.9. For a given base line, which will show a greater parallax - a distant star or a nearby star?****Ans.**** **Parallactic angle, θ = (base line/distance of star) = b/S. Thus for a given base line b, parallax of a star is inversely proportional to its distance S. Hence the nearby star will show a greater parallax.**Q.10. Why is parallax method not useful for measuring the distances of stars more than 100 light years away?****Ans.** For a star more than 100 light years away, the parallax angle is so small that it cannot be measured accurately.**Q.11. What is the difference between mN, Nm and nm?****Ans.**

1 mN = 1 milli newton = 10^{-3} newton (unit of force).

1 Nm = 1 Newton metre (unit of work)

1 nm = 1 nanometre =10^{-9} metre (unit of distance).**Q.12. Do all physical quantities have dimensions? If no, name three physical quantities which are dimensionless.****Ans.** No, all physical quantities do not have dimensions. The physical quantities like angle, strain and relative density are dimensionless.**Q.13. If 'slap' times speed equals power, what will be the dimensional equation for 'slap'?****Ans. **

As slap x speed = power

Slap = (Power/Speed) = (ML^{2}T^{-3}/LT^{-1}) = MLT^{-2}

**Q.14. What is the basis of the principle of homogeneity of dimensions****Ans. **The principle of homogeneity of dimensions is based on the fact that only the physical quantities of the same kind can be added, subtracted or compared.**Q.15. ****If x = a + bt +ct ^{2} where x is in metre and t in second; then what is the unit of c?**

[x] = [ct

or

[c] = [x/t

[a] = [F] = MLT

A = (Unit of v/Unit of t

**Units of **

B = (Unit of v/Unit of t) = ms^{-1}/s = ms^{-2}**Unit of **

C = Unit of v = ms^{-1}.**Q.21. Can a quantity have dimensions but still has no units?****Ans.** No, a quantity having dimensions must have some units of its measurement.**Q.22. Can a quantity have different dimensions in different systems of units?****Ans.** No, a quantity has same dimensions in all system of units.**Q.23. Can a quantity have units but still be dimensionless?****Ans.** Yes. For example, a plane angle has no dimensions but has unit like radian for its measurement.**Q.24. Does the magnitude of a physical quantity depend on the system of units chosen?****Ans.** No. The magnitude of physical quantity remains same in all systems of units.**Q.25. Justify L + L = L and L - L = L.****Ans.** When we add a length to another length, we get length only so L + L = L is justified. When we subtract a length from another length, again we get length. This justifies L − L = L**Q.26. Can there be a physical quantity that has no units and no dimensions?****Ans.** Yes, strain is a physical quantity that has no units and no dimensions.**Q.27. Can an instrument be called precise with-out being accurate? Can it be accurate without being precise?****Ans.** Yes, an instrument can be precise without being accurate but the measurements cannot be accurate without being precise.**Q.28. Which of the following length measurements is ****(i) most precise and ****(ii) least precise? ****Give reason ****(i) l = 5 cm ****(ii) l = 5.00 cm ****(iii) 5.000 cm ****(iv) 5.000 cm ****(v) 5.00000 cm.****Ans.****(i)** The last measurement is most precise, because it has been taken with an instrument whose least count is equal to 0.00001 cm. **(ii)** The first measurement is least precise because it has been taken with a device having least count equal to 1 cm.**Q.29. Which of the following readings is the most accurate: ****(i) 5000 m ****(ii) 5×10 ^{2} m **

(i) 5000 m is most accurate.

1 bar = 1 atmospheric pressure = 760 mm of Hg column

1 torr = 1 mm of Hg column

∴ 1 bar = 760 torr.

Clearly, the error in the measurement of time period T has larger effect on the value of g than the error in the measurement of length l.

Reasons

As LHS ≠RHS, the formula is incorrect.

Dimensionally, m

As LHS ≠ RHS, the formula is incorrect

Dimensionally, m

As LHS = RHS, the formula is correct.

**Q.43 The mean value of period of oscillation of a simple pendulum in an experiment is 2.825 s. The arithmetic mean of all the absolute errors is 0.11 s. Round off the period of simple pendulum to appropriate number of significant figures. Give reasons.**

**Ans.** The absolute error 0.11 s has only two significant figures.

∴ Period of simple pendulum = 2.9 s [Rounded off up to 2 significant figures]

∴ Period of simple pendulum = 2.9 s [Rounded off up to 2 significant figures]

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