# Units, Dimensions and Measurement.

1. If the acceleration due to gravity is 10 ms-2 and the units of length and time are changed in kilometer and hour respectively, the numerical value of the acceleration is
Ans: 129600
Sol: 2. If L, C and R represent inductance, capacitance and resistance respectively, then which of the following does not represent dimensions of frequency
Ans: Sol: does not represent the dimension of frequency

3. Number of particles is given by crossing a unit area perpendicular to X-axis in unit time, where n1 and n2 are number of particles per unit volume for the value of x meant to x2 and x1. Find dimensions of D called as diffusion constant
Ans: M0L2T-1  5. If the dimensions of length are expressed as Gxcyhz; where G,c and h are the universal gravitational constant, speed of light and Planck's constant respectively, then
Ans:  6. A highly rigid cubical block A of small mass M and side L is fixed rigidly onto another cubical block B of the same dimensions and of low modulus of rigidity  such that the lower face of A completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force F is applied perpendicular to one of the side faces of A. After the force is withdrawn block A executes small oscillations. The time period of which is given by
Ans:  7. The pair(s) of physical quantities that have the same dimensions, is (are)
Ans: Reynolds number and coefficient of friction, Latent heat and gravitational potential, Curie and frequency of a light wave 8. The speed of light (c), gravitational constant (G) and Planck's constant (h) are taken as the fundamental units in a system. The dimension of time in this new system should be
Ans: G1/2h1/2c-5/2 9. If the constant of gravitation (G), Planck's constant (h) and the velocity of light (c) be chosen as fundamental units. The dimension of the radius of gyration is
Ans:  h1/2c-3/2G1/2 10. X = 3YZ2 find dimension of Y in (MKSA) system, if X and Z are the dimension of capacity and magnetic field respectively
Ans: M-3L-2T8A4
Sol: 11. In the relation P is pressure, Z is the distance, k is Boltzmann constant and q is the temperature. The dimensional formula of b will be
Ans:  [M0L2T0] 12. The frequency of vibration of string is given by . Here p is number of segments in the string and l is the length. The dimensional formula for m will be
Ans:  [ML-1T0]  Ans:  (i) G, (ii) H, (iii) C, (iv) B, (v) C

14. A wire has a mass 0.3 ∓ 0.003 g, radius 0.5 ∓ 0.005 mm and length 6 ∓ 0.06 cm. The maximum percentage error in the measurement of its density is
Ans: 4 15. If 97.52 is divided by 2.54, the correct result in terms of significant figures is
Ans: 38.4

16. The surface tension of a liquid is 70 dyne / cm. In MKS system its value is
Ans:  7 × 10-2 N /m 17. The SI unit of universal gas constant (R) is
Ans: joule K-1 mol-1
Sol: 18. The unit of permittivity of free space εo is
Ans: Coulomb2 / Newton - metre3 19. The temperature of a body on Kelvin scale is found to be X K. When it is measured by a Fahrenheit thermometer, it is found to be XoF. Then X is
Ans:  574.25 20. What are the units of Ans:  Nm2 C-2
Sol: 21. The SI unit of surface tension is
Ans:  Newton / metre

22.  E, m, l  and G denote energy, mass, angular momentum and gravitational constant respectively, then the dimension of are
Ans:  Angle 23. From the equation , one can obtain the angle of banking θ for a cyclist taking a curve (the symbols have their usual meanings). Then say, it is
Ans:  Dimensionally correct only
Sol:  Given equation is dimensionally correct because both sides are dimensionless but numerically wrong because the correct equation is .

24. A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ή flowing per second through a tube of radius r and length l and having a pressure difference p across its end, is
Ans: Sol:  Formula for viscosity 25. The velocity v ( in cm / sec ) of a particle is given in terms of time t (in sec) by the relation ; the dimensions of a, b and c are
Ans:  a = LT-2, b = L, c = LT
Sol:  From the principle of dimensional homogenity . Similarly 26.  From the dimensional consideration, which of the following equation is correct
Ans: Sol:  By substituting the dimensions in we get 27. The position of a particle at time t is given by the relation , where v0 is a constant and α > 0 . The dimensions of v0 and α are respectively
Ans:  M0L1T-1 and T-1  29.  The dimensions of in the equation , where p is pressure, x is distance and t is time, are
Ans:  MT-2 30. Dimensions of , where symbols have their usual meaning, are
Ans:   [L2T-2]
Sol: 31. The dimensions of , where and c are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum respectively
Ans: [M0L0T0] 32. If radius of the sphere is ( 5.3 ± 0.1 ) cm. Then percentage error in its volume will be
Ans:  33. The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, The maximum error in the measurement of pressure is
Ans:  8% 34. While measuring the acceleration due to gravity by a simple pendulum, a student makes a positive error of 1% in the length of the pendulum and a negative error of 3% in the value of time period. His percentage error in the measurement of g by the relation will be
Ans:  7% 35. The length, breadth and thickness of a block are given by l = 12 cm, b = 6 cm and t = 2.45 cm.  The volume of the block according to the idea of significant figures should be
Ans:  2 × 102 cm3 Assertion Reason

Choose any one of the following four responses :
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

36. Assertion : ‘Light year’ and ‘Wavelength’ both measure distance.
Reason : Both have dimensions of time.
Ans:  Assertion is true but reason is false.
Sol:  Light year and wavelength both represents the distance, so both has dimension of length not of time.

37. Assertion : Light year and year, both measure time.
Reason : Because light year is the time that light takes to reach the earth from the sun.
Ans:   The assertion and reason both are false.
Sol:   Light year measures distance and year measures time. One light year is the distance traveled by light in one year.

38. Assertion : Force cannot be added to pressure.
Reason : Because their dimensions are different.
Ans:   Both assertion and reason are true and the reason is the correct explanation of the assertion.
Sol:   Addition and subtraction can be done between quantities having same dimension.

39. Assertion : Linear mass density has the dimensions of [M1L–1T0].
Reason : Because density is always mass per unit volume.
Ans:   Assertion is true but reason is false.
Sol:   Density is not always mass per unit volume.

40. Assertion : Rate of flow of a liquid represents velocity of flow.
Reason : The dimensions of rate of flow are [M0L1T–1].
Ans: The assertion and reason both are false.
Sol: Rate of flow of liquid is expressed as the volume of liquid flowing per second and it has dimension  [L3T–1].

41. Assertion : Units of Rydberg constant R are m–1
Reason : It follows from Bohr’s formula , where the symbols have their usual meaning.
Ans:   Both assertion and reason are true and the reason is the correct explanation of the assertion.

42. Assertion : Parallex method cannot be used for measuring distances of stars more than 100 light years away.
Reason : Because parallex angle reduces so much that it cannot be measured accurately.
Ans:  Both assertion and reason are true and the reason is the correct explanation of the assertion.
Sol:  As the distance of star increases, the parallax angle decreases, and great degree of accuracy is required for its measurement. Keeping in view the practical limitation in measuring the parallax angle, the maximum distance of a star we can measure is limited to 100 light year.

43. Assertion : Number of significant figures in 0.005 is one and that in 0.500 is three.
Reason : This is because zeros are not significant.
Ans:  Assertion is true but reason is false.
Sol:  Since zeros placed to the left of the number are never significant, but zeros placed to right of the number are significant.

44. Assertion : Out of three measurements l = 0.7 m; l = 0.70 m and l = 0.700 m, the last one is most accurate.
Reason : In every measurement, only the last significant digit is not accurately known.
Ans:   Both assertion and reason are true but reason is not the correct explanation of the assertion.
Sol:  The last number is most accurate because it has greatest significant figure (3).

45. Assertion : Mass, length and time are fundamental physical quantities.
Reason : They are independent of each other.
Ans: Both assertion and reason are true and the reason is the correct explanation of the assertion.
Sol:  As length, mass and time represent our basic scientific notations, therefore they are called fundamental quantities and they cannot be obtained from each other.

46. Assertion : Density is a derived physical quantity.
Reason : Density cannot be derived from the fundamental physical quantities.
Ans:   Assertion is true but reason is false.
Sol:  Because density can be derived from fundamental quantities.

47. Assertion : Now a days a standard metre is defined as in terms of the wavelength of light.
Reason : Light has no relation with length.
Ans: Assertion is true but reason is false
Sol:  Because representation of standard metre in terms of wavelength of light is most accurate.

48.  Assertion : Radar is used to detect an aeroplane in the sky
Reason : Radar works on the principle of reflection of waves.
Ans: Both assertion and reason are true and the reason is the correct explanation of the assertion.
Sol:  As radar is most accurate instrument used to detect aeroplane in sky based on principle of reflection of radio waves.

49. Assertion : Surface tension and surface energy have the same dimensions.
Reason : Because both have the same S.I. unit
Ans: Assertion is true but reason is false.
Sol:  As surface tension and surface energy both have different S.I. unit and same dimensional formula.

50. Assertion : In is dimensionless.
Reason : Because dimension of Ans: Assertion is true but reason is false.
Sol:  As ω (angular velocity) has the dimension of [T-1] not [T].

51. Assertion : Radian is the unit of distance.
Reason : One radian is the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.
Ans: Both assertion and reason are true but reason is not the correct explanation of the assertion.
Sol: Radian is the unit of plane angle

52. Assertion : A.U. is much bigger than Aº.
Reason : A.U. stands for astronomical unit and Aº stands from Angstrom
Ans: Both assertion and reason are true but reason is not the correct explanation of the assertion.
Sol: A.U. is used (Astronomical units) to measure the average distance of the centre of the sun from the centre of the earth, while angstrom is used for very short distances. 1 A.U. =  1.5 × 1011 m: 1Aº = 10-10 m

53. Assertion : When we change the unit of measurement of a quantity, its numerical value changes.
Reason : Smaller the unit of measurement smaller is its numerical value.
Ans:  Assertion is true but reason is false.
Sol:  We know that Q = n1u1 = n2u2 are the two units of measurement of the quantity Q and n1, n2 are their respective numerical values. From relation Q = n1u1 = n2u2  nu = constant i.e., smaller the unit of measurement, greater is its numerical value.

54. Assertion : Dimensional constants are the quantities whose value are constant.
Reason : Dimensional constants are dimensionless.
Ans:  Assertion is true but reason is false.
Sol:  Dimensional constants are the quantities whose value are constant and they posses dimensions. For example, velocity of light in vacuum, universal gravitational constant, Boltzman constant, Planck’s constant etc.

55. Assertion : The time period of a pendulum is given by the formula, Reason : According to the principle of homogeneity of dimensions, only that formula is correct in which the dimensions of L.H.S. is equal to dimensions of R.H.S.
Ans:  Assertion is false but reason is true. 56. Assertion : In the relation where symbols have standard meaning, m represent linear mass density.
Reason : The frequency has the dimensions of inverse of time.

Ans:  Both assertion and reason are true but reason is not the correct explanation of the assertion. 57. Assertion : The graph between P and Q is straight line, when P/Q is constant.
Reason : The straight line graph means that P proportional to Q or P is equal to constant multiplied by Q.
Ans:  Both assertion and reason are true and the reason is the correct explanation of the assertion. 58. Assertion : Avogadro number is the number of atoms in one gram mole.
Reason : Avogadro number is a dimensionless constant.
Ans:  Assertion is true but reason is false.
Sol:  Avogadro number (N) represents the number of atoms in 1 gram mole of an element, i.e. it has the dimensions of mole-1.

59. Assertion : L/R and CR both have same dimensions.
Reason : L/R and CR both have dimension of time.
Ans:  Both assertion and reason are true and the reason is the correct explanation of the assertion. 60. Assertion : The quantity is dimensionally equal to velocity and numerically equal to velocity of light.
Reason : μ0 is permeability of free space and ϵ0 is the permittivity of free space.
Ans:  Both assertion and reason are true but reason is not the correct explanation of the assertion. Posted Date : 17-02-2021

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గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.