UNIT & MEASUREMENT

CHAPTER :- UNIT & MEASUREMENT

(SECTION-A)

1. Which of the following dimensional formula is/are correct.

(A) [permittivity of the free space × electric field] = [Mº L^–2 T¹ A¹ ]

(B) [electrical conductivity] = [M^–1 L^–3 T³ A¹]

(D) = [Mº L¹ T^–3 ]

2. If we define a new system of units in which the unit of length is double that of present unit then the numerical value of m₀ (permeability of free space) will become

(A) half (B) double

3. For a cubical block, error in measurement of sides is + 1% and error in measurement of mass is + 2%, then maximum possible error in density is -

(A) 1% (B) 5%

4 Kerosene oil is flowing through a tube of length l & radius r . The pressure difference between two ends of the tube is P, then the viscosity of oil is given by h = where v is velocity of oil at a distance x from the axis of tube . From this relation the dimensions of viscosity h are :

(A) ML²T² (B) ML-¹T-¹

5 The density of cube is measured by measuring its mass and length of the side . If the maximum errors in the measurement of mass and length are 4 % & 1 % respectively , the maximum error in the measurement of density is :

(A) 2 % (B) 5 %

6 An experiment measures quantities a, b, c. Another quantity X is calculated from the formula, X = . If the percentage errors in a, b & c are ± 1 %, ± 3 % & ± 2 % respectively the maximum percentage error in X will be :

(A) ± 13 % (B) ± 7 %

7. Match the physical quantities given in column I with dimensions expressed in terms of mass (M), length (L), time (T) and charge (Q) given in column II and write the correct answer against the matched quantity.

Column I Column II

(i) Angular momentum (a) ML² T^–2

(ii) Latent heat (b) ML²Q^–2

(iii) Torque (c) ML²T^–1

(iv) Capacitance (d) ML³ T^–1 Q^–2

(v) Inductance (e) M^–1 L^–2 T² Q²

(vi) Resistivity (f) L² T^–2

(A) (i) - (c) (B) (ii) - (d)

8 A watt is :

(A) kg m/s² (B) kg m²/s³

9 Kilowatt-hour is a unit of

(A) Power (B) Energy/time

10. Experiment shows that two perfectly neutral parallel metal plates separated by a small distance d, attract each other via a very weak force, known as the Casimir force. The force per unit area of the plates, F, depends only on the Planck constant h, on the speed of light c, and on d. Which of the following has the best chance of being correct for F ?

(A) F = (B) F =

11. Which of the following quantity has the dimension of length.

(A)

(B)

(C)

(D)

12 Time period of oscillation of the surface of a small drop of liquid depends on density r, radius r and surface tension s. The surface tension of a free liquid surface is defined as force per unit length. The dependence of time period can be given by

(A) T a (B) T a rrs

13. The surface tension and bulk modulus of elasticity of water are S and B respectively. Then the ratio is dimensionally equivalent to the dimension of

(A) Length (B) Wave number

14. Due to explosion under water, a gas bubble is formed which oscillates with a Time Period T. Experimentally, it was found that T is proportional to P^a d^b E^c, where P is the static pressure, d is the density and E is the total energy of explosion.The values of a, b and c are:

(A) a = 0, b = 1, c = 2

(B) a = 1, b = 2, c = 1

(D) a = , b = , c =

15. The S.I. unit of inductance henry can not be written as :

(A) Weber/ampere

(B) Volt second/ampere

(D) Ohm/sec

16. The readings of a constant potential difference is noted four times by a student. The student averages these readings but does not take into account the zero error of the voltmeter. The average measurement of the potential difference is

(A) precise and accurate

(B) precise but not accurate

(D) not accurate and not precise

17. A vernier calipers which is used to measure length of a cylinder has 1mm marks on the main scale. It has 10 equal division on the vernier scale which match with 8 marks of main scale. If main scale reading is 4 and vernier reading is 5 then the length of cylinder is 1.25 N × 10^–3 m then calculate N :

(A) 3 (B) 4 (C) 7 (D) 2

18. An unknown quantity x is measured using an experiment by measuring a length l(in cm) from scale having least count of 1cm. Formula used is x = R . R is known accurately. Find the percentage error in measurement of 'x' for l = 50 cm.

(A) 4 (B) 7 (C) 9 (D) 12

19. The length and breadth of a rectangle are (6.0 0.3) cm and (4.0 0.2) cm. Then the area of the rectangle with error limits is :

(A) 26 cm² (B) (24 ± 2) cm²

20. Assertion : Distance is always a non negative quantity.

Reason : Distance is a scalar quantity.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

(D) Statement-1 is False, Statement-2 is True.

21. Assertion : The numerical value of a physical quantity remains same in every system of units.

Reason : The product of the numerical value and unit of a physical quantity remains same in any system of units.

(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

(D) Statement-1 is False, Statement-2 is True.

22. Which of the following is not the unit of length :

(A) micron (B) light year

23. Unit of Stefan’s constant is :-

(A) Watt–m² –K⁴ (B) Watt–m² –K⁴

24. If n is number and u is the unit of a physical quantity then which of the following is correct for the measurement of "n"-

(A) n µ size of u (B) n µ u²

25. In C.G.S. system the magnitude of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, meter and minute, the magnitude of the force is-

(A) 0.036 (B) 0.36

26. The units of angular momentum are-

(A) kg-m²/s² (B) joules-s

27. The ratio of S.I. units to the C.G.S units of ‘G’ is -

(A) 10^–2 (B) 10^–3

28. If the units of M & L are doubled then the unit of kinetic energy will become -

(A) 8 times (B) 16 times

29. Unit of impulse is :

(A) Newton (B) kg-m

30. The unit of permittivity of free space e is :-

(A) Newton metre²/Coulomb²

(B) Coulomb/Newton metre

(D) Coulomb² / (Newton metre)²

31. Which of the following set have different dimensions ?

(A) Pressure, Young’s modulus, Stress

(B) Emf, Potential difference, Electric potential

(D) Dipole moment, Electric flux, Electric field

32. Pressure gradient has the same dimesion as that of

(A) Velocity gradient

(B) Potenital gradient

(D) None of these

33. “ Pascal -Second ‘’has dimension of

(A) Force

(B) Energy

(D) Coefficient of Viscosity

34. Which relation is wrong

(A) 1 Calore = 4.18 Joules

(B) 1Å = 10^-10 m

(D) 1 Newton =10 ^-5 Dynes

35. In a given relation F = at¹ + bt², F and t denote the force and the time respectively, then dimensions of a and b are respectively as –

(A) M°L°T¹, M°L°T^–2

(B) M°L¹T^–2, M°L²T^–2

(D) M¹L¹T^–1, M¹L¹T^–2

36. Dimensions of Torque are-

(A) M¹L²T^–2 (B) M²L²T²

37. Which of the following is dimensionless -

(A) universal gravitational constant

(B) relative permittivity

(D) density

38. What will be the unit of c in the equation S = a + bt + ct² if the units of S and t are meter and second respectively -

(A) meter (B) meter-sec^–1

39. In a system of unit if force (F), acceleration (A) and time (T) are taken as fundamental units then the dimensional formula of energy is :

(A) FA²T (B) FAT²

40. In the previous question, minimum possible error in area measurement can be -

(A) + 0.02 cm² (B) + 0.01 cm²

41. The least count of a stop watch is 0.2 second. The time of 20 oscillations of a pendulum is measured to be 25 seconds. The percentage error in the time period is

(A) 16% (B) 0.8 %

42. The mass of a ball is 1.76 kg. The mass of 25 such balls is

(A) 0.44 × 10³ kg (B) 44.0 kg

43. Two resistors R₁ (24 ± 0.5) W and R₂ (8 ± 0.3) W are joined in series. The equivalent resistance is

(A) 32 ± 0.33 W (B) 32 ± 0.8 W

44. In an experiment, the percentage of error occurred in the in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = , will be

(A) 10 % (B)

45. The dimension of , where e₀ is permittivity of free space and E is electric field, is

(A) ML²T^–2 (B) ML^–1T^–2

46. If force (F), velocity(V) and time (T) are taken as fundamental units, the dimensions of mass are

(A) [FVT^–1] (B) [FVT^-2]

47. The dimension of are

(A) (B)

48. "Pascal-Second" has dimension of

(A) Force

(B) Energy

(D) Coefficient of viscosity

49. The ratio of the dimension of Planck's constant and that of moment of inertia is the dimension of

(A) Frequency (B) Velocity

50. The period of oscillation of a simple pendulum is given by where l is about 100 cm and is known to have 1mm accuracy. The period is about 2s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is

(A) 0.1% (B) 1%

NEET ANSWER KEY & SOLUTIONS

SUBJECT :- PHYSICS

CLASS :- 11^th PAPER CODE :- CWT-1

CHAPTER :- UNIT & MEASUREMENT

ANSWER KEY

1. (A) 2. (A) 3. (B) 4. (B) 5. (D) 6. (A) 7. (A)

8. (B) 9. (C) 10. (B) 11. (A) 12. (A) 13. (B) 14. (D)

15. (D) 16. (B) 17. (B) 18. (A) 19. (D) 20. (B) 21. (D)

22. (D) 23. (D) 24. (D) 25. (C) 26. (B) 27. (D) 28. (A)

29. (C) 30. (C) 31. (D) 32. (D) 33. (D) 34. (D) 35. (C)

36. (A) 37. (B) 38. (C) 39. (B) 40. (D) 41. (B) 42. (B)

43. (B) 44. (C) 45. (B) 46. (D) 47. (C) 48. (D) 49. (A)

50. (C)

SOLUTIONS

SECTION-A

1. (A)

2. (A)

3. (B)

Sol.

Given 2% = ± 2 × 10^–2 = ± 1% = ± 1 × 10^–2

= 2 × 10^–2 + 3 × 10^–2 = 5 × 10^–2 = 5%

4. (B)

Sol. [h] = = ML^–1T^–1.

5. (D)

6. (A)

7. (A)

Sol. For angular momentum.

L = Mvr = M (LT^–1) (L) = ML²T^–1 ® (c)

8. (B)

Sol. Watt = = = kg

9. (C)

Sol. kwh Þ energy or work

10. (B)

Sol. F =

= joule-sec. = = Newton

. Hence F = hc/d⁴

= Newton-metre² sec²

11. (A)

Sol. Young modulus º pressure º P (say)

Coefficient of viscosityº º

Surface tension º

\ º L º length

12. (A)

Sol. Let T a r^a

a r^b

a s^c

Þ T = K r^a r^b s^c

Þ [T] = [ML^–3]^a × [L]^b [MT^–2]^c

= [M^{a + c} L^{–3a + b} T^–2c ]

Þ a + c = 0 ; – 3a + b = 0 , – 2c = 1

Þ a = + , b = ; c = –

Þ T a

13. (B)

Sol. = × = = wave number

14. (D)

Sol. T µ P^a d^b E^c

T = K P^a d^b E^c

where k is a dimensionless constant.

[Mº Lº T’] = [ML^–1T^–2]^a [ML^–3]^b [ML² T^–2]^c

[Mº Lº T¹] = [M^{a + b + c} L^{–a – 3b + 2c} T^{–2a – 2C}]

Comparing dimensions of both sides

a = , b = , c =

15. (D)

16. (B)

Sol. Averaging a number of readings makes the measurement more precise.

17. (B)

Sol. Least count = 1 – = 0.2 mm

Length = 4 + 5 × 0.2 = 5.0 mm

= 5.0 × 10^–3 m.

18. (A)

Sol. x =

× 100 = × 100 = 4%.

19. (D)

Sol. Here A = 24.0

± = 0.1

Þ DA = ±2.4

So, Area = (24.0 ± 2.4) cm²

20. (B)

21. (D)

Sol. The product of numerical value and unit of a physical quantity remains same in any system of units, hence numerical value of a physical quantity will be different for different units.

for example 1 metre = 100 cm.

Hence statement 1 is false.

22. (D)

Sol. Micron, light year & angstrom are units of length and radian is unit of angle.

23. (D)

Sol. According to Stefan's law,

E µ T⁴

orE = sT⁴

Here, s is proportionality constant called the Stefan's constant.

The unit of stefan's constant is watt metre ^–2 kelvin^–4 or W/m²-K^4.

24. (D)

Sol. n u = constant so n µ

25. (C)

Sol. n₁ u₁ = n₂ u₂

n₂ = n₁ = n₁

n₂ = 100 = 3.6

26. (B)

Sol. Angular momentum L = mvr

(L) = (kg) . (m) = kg m² s^–1

(L) = (kg m² s^–2). (s) = Joule – s

27. (D)

Sol. [G] = [M^–1 L³ T^–2] Þ

1 SI = 1000 CGS

= 1000

28. (A)

Sol. KE. = mV²

[KE] = ML² T^–2]

If unit of M and L are doubled

Then unit of K.E.

K.E. = [(2M) (2L)² T^–2]

= 8 [ML² T^–2]

unit of K.E. is 8 times.

29. (C)

30. (C)

Sol. Substitute the units for all the quantities involved in an expressioin written for permittivity of free space.

By coulomb's law, the electrostatic force

Substituting the units for q, and F, we obtain unit of

= C²/ N-m²

31. (D)

Sol. [Dipole moment] = LIT, [f_E] = ML³ /IT³ [E] = ML/IT³.

32. (D)

33. (D)

34. (D)

35. (C)

Sol. F = at⁺¹ + bt⁺²

[a] = = [MLT^–3]

[b] = = [MLT^–4]

SECTION-B

36. (A)

Sol. [t] = [F. r]

[MLT^–2.L] = [ML²T^–2]

37. (B)

Sol. (A) [G] = [M^–1 L³T^–2]

(B) e_r = unit less and dimension less

because e and e₀ are permittivity of medium and vaccum having same dimensions.

(D) Density = ML^–3

38. (C)

Sol. S = a + bt + c t²

unit of C = unit of = metre sec^–2= [work]

39. (B)

Sol. E = k F^a A^b T^c

[ML²T^–2] = [MLT^–2]^a [LT^–2]^b [T]^c

[ML²T^–2] = [M^aL^a+b T^{–2a – 2b + c}]

a = 1, a + b = 2, –2a – 2b + c = – 2

a = 1, b = 1, c = 2

40. (D)

Sol. = = = 0

41. (B)

Sol. Dt = 0.2 s.

t = 25 s

T = Þ = = = 0.8 %

42. (B)

Sol. m = 1.76 kg

M = 25 m

= 25 × 1.76

= 44.0 kg

Note : Mass of one unit has three significant figures and it is just multiplied by a pure number (magnified). So result should also have three significant figures.

43. (B)

Sol. R₁ = (24 ± 0.5) W

R₂ = (8 ± 0.3) W

R_S = R₁ + R₂

= (32 ± 0.8) W

44. (C)

Sol. x =