Chapter 2 UNITS AND MEASUREMENT 1) What is a physical quantity? The quantity which can be measured and given in terms of numerical value is called physical quantity. 2) Name the types of physical quantities. • Fundamental quantity or base quantity • Derived quantity 3) Define fundamental(base) physical quantity. The quantities which are independent of other physical quantities are called fundamental quantities. Examples : Length, Mass, Time, Temperature, Electrical current, Luminous intensity and Amount of substance. 4) Define derived quantities. The quantities which are derived from fundamental quantities are called derived quantities. Examples : Speed, Velocity, Acceleration, Force etc. 5) Define unit. The standard quantity in terms of which a physica l quantity can be measured is called unit of that physical quantity. 6) What are fundamental or base units? Units for fundamental quantities are called fundamental units. 7) What are derived units? U nits for derived quantities are called derived units. 8) What is system of units? A complete set of fundamental and derived units for all physical quantities is called system of units. 9) Explain SI System. [Bengaluru 2017] The system of unit which is internationally accepted at present for the measurement of physical quan tities is called SI system (international system). It consists of seven base units, two supplementary units and many derived units Types of System of Units : System Length Mass Time CGS centimeter gram second FPS foot pound second MKS meter kilogram second SI System for base or fundamental quantities: Quantity U nit Definition Symbol Dimensional formula L ength meter The meter is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second. m [L] Mass kilogram The kilogram is equal to the mass of the international prototype of the kilogram i.e.., a platinum - iridium alloy cylinder kept at international Bureau of Weights and Measures, at Sevres, near Paris, France. kg [M] Time second The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium - 133 atom. s [T] Temperature kelvin The kelvin, is the fraction 1/273.16 of the t hermodynamic temperature of the triple point of water. K [K] Electric current ampere The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross - section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2×10 – 7 newton per meter of length. A [A] Luminous Intensity candela The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×10 12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. cd [J] Amount of Substance mole The mole is the amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon - 12. mol [ mol ] 10) Give Relation between Physical quantity (Q), numerical value (n) and unit (U). Q = nU 11) Name supplementary quantities? Plane angle and solid angle are called supplementary quantities. 12) Define plane angle. [D.K 2013] It is the ratio of length of arc to the radius of a circle. d = arc length radius = ds r • SI unit of Plane angle is radian and its symbol is rad • 1º= π 180 rad = 1 74 x 10 − 2 rad • 1º=60' • 1'=2.9x10 - 4 rad • 1'=60'' • 1''=4.85x 10 - 6 rad Problems: 1. Calculate the angle of a) 1 0 (degree) b) 1′ (minute of arc or arcmin) c) 1′′ (second of arc or arc secon D) in radians. (Use 360 0 =2π rad, 1 0 =60′ and 1′ = 60 ′′) 13) Define solid angle. [Chikkamagaluru 2016] It is the ratio of the intercepted area dA of the spherical surface to the square of the radius. dΩ = ( intersepted area ) radius 2 = dA r 2 SI unit of solid angle is steradian and its symbol is sr. Plane angle and Solid angle both are dimensionless quantities. 14) Mention the conditions to choose a unit of physical quantity. • It should be internationally accepted. • It must be well defined. • It should be easily reproducible • It should not change with time and other physical conditions. 15) What are the rules to write a unit? • When a unit is named after a person(scient ist), the unit is not written with a capital initial letter but the symbol is a capital letter. Example: The unit of force is “newton (N)” The unit of power is “watt (W)” • If the unit is not named after a person, both the unit as well as its symbol are not written in capital let- ters. Example: The unit of mass is “kilogram (kg)” The unit of length is “meter (m)” • The symbols of units are not expressed in plural form, full stops and other punctuation marks. 16) List the rules o f significant figures • All non - zero digits are significant. Ex: 2453 has 4 significant figures • All zeros between two non - zero digit are significant. Ex :24053 has 5 significant figures • All zeros occurring between the decimal point and first non - zero digi ts are not significant. Ex: 0.0024053 has 5 significant figures • Trailing zeros in a number with a decimal point are significant. Ex: 24053.00 has 7 significant figures and 0.06900 has 4 significant figures • Trialing zeros in a number without the decimal poi nts are not a significant, but if the zero is a result of measurement, then it is significant. Ex: 2400 has 2 significant If 2400 is a measurement of a physical quantity say length of the road is 2400m then it has 4 significant figures. • An exponential term does not contribute towards the significant. Ex: 2.456x10 5 has 4 significant figures. • Exact numbers are having infinite significant figures. Ex: 10 pens have infinite significant figures. 17) What is the rule of significant figures in addition and subtraction? In addition, and subtraction, the final result should retain as many decimal places as are there in the number with least decimal places. Ex: 436.32+ 227.2 +0.301=663.821 Here the least precise measurement is 227.2 is correct to o ne decimal place. Hence the final result should be rounded off to 663. 8 18) What is the rule of significant figures in multiplication or division? In multiplication or division, the final result should retain as many significant figures as are there in the o riginal number with the least significant figures. Ex: Let density = 4 237 2 51 = 1 68804780876 𝑔 𝑐𝑚 − 1 Using the division rule above result should be rounded off to 1.69 gcm - 1 19) Write the rules for rounding of the uncertain digit. T he preceding digit is raised by 1 if the uncertain digit to be dropped is more than 5 and if left unchanged if the latter is less than 5. Example 1: Round off 5.686 to 3 significant figures. Ans: 5.69 Example 2: Round off 5.683 to 3 significant figures. Ans: 5.68 If the uncertain digit to be dropped is 5, the preceding digit raised by 1 if it is odd and is left unchanged if it is even. Example 1: Round off 7.735 to 3 significant figures Ans: 7.74 Ex 2: Round o ff 7.745 to 3 significant figures Ans: 7.74 Problems: 1. Each side of a cube is measured to be 7.203 m. What are the total surface area and the volume of the cube to appropriate significant figures? (Ans: Surface area = 311.3m 2 Volume = 373.7m 3 ) 2. State the n umber of significant figures in the following: A) 0.007 m 2 B) 6.320 J C) 2.64 × 10 24 kg D) 6.032 N m – 2 E ) 0.2370 g cm – 3 F ) 0.0006032 m 2 3. The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m, and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures. (Ans: Area = 8.72m 2 ; Volume = 0.0855m 3 ) 4. The mass of a box measured by a grocer’s balance is 2.300 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is A) the total mass of the box, B) the difference in the mass- es of the pieces to correct significant figures (Ans: M = 2.3kg; Δm = 0. 02g ) 20) Define dimensions. The dimensions of a physical quantity are the power to which the base quantities are raised to represents that quantity. Example: Force F = [ M 1 L 1 T − 2 ] here dimensions of force is 1 in mass, 1 in length and - 2 in time. 21) What is dimensional formula? The expression which shows how and which of the base quantities represents dimensions of a physical quantity is called dimensional formula. It is expressed in [ ] square bracket. Ex: Dimensional Formula of Force is F = [ M 1 L 1 T − 2 ] 22) What is dimensional equation ? An equation by equating a physical quantity with its dimensional formula is called dimensional equation. Dimensional equation of Force is [ F ] = [ M 1 L 1 T − 2 ] 23) What i s dimensional constant ? C onstants which possess dimensions are called dimensional constants. Ex: Gravitational constant [ G ] = [ M − 1 L 3 T − 2 ] Planck’s constant [ h ] = [ M 1 L 2 T − 1 ] 24) What are dimensionless quantities? [ D.K 2014] The quantities which do not possess dimensi ons are called dimensionless quantities. Examples: Plane angle, strain, refractive index etc. 25) Mention Principle of Homogeneity of Dimensions T he dimensions of all terms on the two sides of an equation must be the same. Principle of homogeneity of dimensions signifies that magnitude of physical quantities may be added to- gether or subtracted from one another only if they have same dimensions. Phy sical quantities and their dimension formula: Physical Quantity Formula Dimensional Formula Speed Speed = Distance Time [M 0 LT - 1 ] Velocity Velocity = Displacement Time [M 0 LT - 1 ] Acceleration Acceleration = Change in velocity Time [M 0 LT - 2 ] Force Force=mass x acceleration [MLT - 2 ] Impulse Impulse=Force x time [MLT - 1 ] Area Area =Length x Length [M 0 L 2 T 0 ] Volume Volume=Length x Length x Length [M 0 L 3 T 0 ] Density Density = Mass Volume [ML - 3 T 0 ] Frequency Frequency = 1 Time [M 0 L 0 T - 1 ] Work Work=Force x Displacement [ML 2 T - 2 ] Energy Energy = 1 2 mv 2 [ML 2 T - 2 ] Power Power = Work Time [ML 2 T - 3 ] Momentum Momentum = mass x velocity [MLT - 1 ] Pressure Pressure = Force Area [ML - 1 T - 2 ] Stress Stress = Force Area [ML - 1 T - 2 ] Strain Strain = Change in length Original Length [M 0 L 0 T 0 ] Young’s Modulus Young ′ s Modulus = Stress Strain [ML - 1 T - 2 ] Surface Tension Surface Tension = Force Length [ML 0 T - 2 ] Surface Energy Surface Energy = Energy Area [ML 0 T - 2 ] Pressure Energy Pressure Energy = Pressure x Volume [ML 2 T - 2 ] Plane Angle Plane angle = Arc length Radius [M 0 L 0 T 0 ] Solid angle Solid angle = Intercepted Area Radius 2 [M 0 L 0 T 0 ] Gravitational Constant G = 𝐹 𝑟 2 𝑚 1 𝑚 2 [M - 1 L 3 T - 2 ] Planck Constant h = 𝐸 𝛾 [M L 2 T - 1 ] 26) Mention the applications of Dimension Analysis. [ D.K 2013, Chitra Durga 2016, Hassan 2017] • To check the correctness of an equation. • To deduce the relation connecting between different physical quantities. • To convert the unit of physical quantity from one system into another system. 27) Check v = v 0 +at where v = final velocity, v 0 = initial velocity, a = acceleration, and t = time is dimen- sionally correct or not. [Udupi 2016, D.K 2016] Dimensional formula of [V] = [M 0 LT - 1 ] [V 0 ] = [M 0 LT - 1 ] [at] = [M 0 LT - 2 T] = [M 0 LT - 1 ] Here each term on RHS of the equation has the same dimensional formula as that of LHS of the equation. Hence it is dimensionally correct. 28) Check the equation X = v 0 t+ 𝟏 𝟐 at 2 is dimensionally correct or not. Where X = displacement, v 0 = initial velocity, a = acceleration, and t = time. [Udupi 2016, D.K 2016] The dimensional formula of [ X ] = [M 0 LT 0 ] [ v 0 t] = [M 0 LT - 1 T] = [M 0 LT 0 ] [ 1 2 at 2 ] = [M 0 LT - 2 T 2 ] = [M 0 LT 0 ] Here each term on RHS of the equation has the same dimensional formula as that of LHS of the equation. Hence above equation is dimensionally correct. 29) Check the correctness of an equation v 2 = v 0 2 +2a X Dimensional formula of [ v 2 ] = [LT - 1 ] 2 = [L 2 T - 2 ] [ v 0 2 ] = [LT - 1 ] 2 = [L 2 T - 2 ] [2a X ] = [LT - 2 ] [L] = [L 2 T - 2 ] Here each term on RHS of the equation has the same dimensional formula as that of LHS of the equation. Hence above equation is dimensionally correct. 30) Derive 𝐓 = 𝟐𝛑 √ 𝒍 𝒈 using dimensional analysis Or The time period of oscillation T of a pendulum is found to depend on m ass(m) of the pendulum , l ength (l) of the pendulum , a cceleration due to gravi- ty(g) at a place. Derive the relation between these physical quantities using dimensional analysis. Time period of oscillation of a simple pendulum depends on its length ( l ), mass of the bob(m) and acceleration due to gravity(g). Then drive the relation connecting between them. Given Tα l x m y g z T = k l x m y g z Write the dimensional formula of all terms [M 0 L 0 T 1 ] = [L] x [M] y [LT - 2 ] z Compare M: M 0 = M y y = 0 Compare L: L 0 = L 𝑥 + 𝑧 x+z = 0 Compare T: T 1 = 𝑇 − 2z - 2z = 1 𝑧 = − 1 2 Then x+z = 0 Then 𝑥 = − 𝑧 = 1 2 Then T = k l 1 2 ⁄ m 0 g − 1 2 ⁄ Then T = k l 1 2 ⁄ g 1 2 ⁄ Then T = k √ 𝑙 𝑔 Where k a constant of proportionality and its value experimentally is 2π Therefore T = 2π √ 𝑙 𝑔 31) The centripetal force (F) acting on a particle moving uniformly in a circle depends upon its mass (m), velocity (v) and radius (r). Derive the exp ression for centripetal force using method of dimen- sions. Given Force F ∝ m x v y r z F = k m x v y r z Writing dimensional formula for all terms [ M 1 L 1 T − 2 ] = [ M ] x [ LT − 1 ] y [ L ] z Compare M: 𝑀 1 = 𝑀 𝑥 x = 1 Compare L: 𝐿 1 = 𝐿 𝑦 + 𝑧 y+z = 1 Compare T: 𝑇 − 2 = 𝑇 − 𝑦 y = 2 Then z = - 1 Then F = k m 1 v 2 r − 1 Then F = k mv 2 r Where k a constant of proportionality and its value experimentally is 1. Therefore F = mv 2 r 32) Convert unit of force from CGS to MKS system. Unit of force in CGS system is dyne and MKS system is newton. Dimensional formula of force [ M 1 L 1 T − 2 ] Let L 1 , M 1 and T be the length, mass and time in MKS system and L 2 , M 2 and T be length, mass and time in CGS system. Then 1 newton = n dyne 𝑛 = 1 𝑛𝑒𝑤𝑡𝑜𝑛 1 𝑑𝑦𝑛𝑒 𝑛 = 𝑀 1 𝐿 1 𝑇 − 2 𝑀 2 𝐿 2 𝑇 − 2 𝑛 = 1000 𝑔 × 100 𝑐𝑚 1 𝑔 × 1 𝑐𝑚 n = 10 5 Then 1newton = 10 5 dyne 33) Convert MKS Unit of work i.e., joule into CGS unit of work i.e., erg. Let L 1 , M 1 and T 1 be the length, mass and time in MKS system and L 2 , M 2 and T 2 be length, mass and time in CGS system Let MKS unit of work = n x CGS unit of work [ 𝑀 1 𝐿 1 2 𝑇 1 − 2 ] = 𝑛 [ 𝑀 2 𝐿 2 2 𝑇 2 − 2 ] 𝑛 = [ 𝑀 1 𝐿 1 2 𝑇 1 − 2 ] [ 𝑀 2 𝐿 2 2 𝑇 2 − 2 ] 𝑛 = 𝑘𝑔 𝑚 2 𝑠 − 2 𝑔𝑐 𝑚 2 𝑠 − 2 = 𝑘𝑔 𝑚 2 𝑠 − 2 10 − 3 𝑘𝑔 10 − 4 𝑚 2 𝑠 − 2 = 1 10 − 7 n = 10 7 Then 1 joule = 10 7 erg. Problems: 1. Let us consider an equation 𝑚𝑣 2 2 = 𝑚𝑔 ℎ , where m is the mass of the body, v its velocity, g is the ac- celeration due to gravity and h is the height. Check whether this equation is dimensionally correct. 2. The SI unit of energy is J = kg m 2 s – 2 ; that of speed v is m s – 1 and of acceleration a is ms – 2 . Which of the formulae for kinetic energy (K) given below can you rule out on the basis of dimensional argu- ments (m stands for the mass of the body): a) K = m 2 v 3 ( Ans: [M 2 L 3 T - 3 ]) b) K = (1/2) mv 2 ( Ans: [ML 2 T - 2 ]) c) K = ma ( Ans: [MLT - 2 ]) d) K = (3/16) mv 2 ( Ans: [ML 2 T - 2 ]) e) K = (1/2) mv 2 + ma ( Ans: I t has no proper dimension) 3. Fill in the blanks a) The volume of a cube of side 1 cm is equal to ...............m 3 (Ans: 10 - 6 ) b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ............. (mm) 2 (Ans: 1.5×10 4 ) c) A vehicle moving with a speed of 18 km h – 1 covers............m in 1s (Ans: 5) d) The relative density of lead is 11.3. Its density is ...............g cm – 3 or ...............kgm – 3 (Ans:11.3, 1.13×10 4 ) 4. Fill in the blanks by suitable conversion of units a) 1 kg m 2 s – 2 = ............. g cm 2 s – 2 (Ans: 10 7 ) b) 1 m = ............. ly (Ans: 10 - 16 ) c) 3.0 m s – 2 = ............... km h – 2 (Ans: 3.9×10 4 ) d) G = 6.67 × 10 – 11 N m 2 (kg) – 2 = ............ (cm) 3 s – 2 g – 1 (Ans: 6.67×10 - 8 ) 5. A book with many printing errors contains four different formulas for the displacement y of a particle undergoing a certain periodic motion: a) y = a sin 2π t/T b) y = a sin vt c) y = (a/T) sin t/a d) y =a/ √ 2 (sin 2πt/T + cos 2πt /T) (a = maximum displacement of the particle, v = speed of the particle. T = time - period of motion). Rule out the wrong formulas on dimensional grounds. (Ans: ‘b’ and ‘c’ are wrong according to dimensional analysis) 6. A famous relation in physics relates ‘moving m ass’ m to the ‘rest mass’ m o of a particle in terms of its speed v and the speed of light, c. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put th e con- stant c. He writes: m = m 0 ( 1 − v 2 ) 1 2 Guess where to put the missing c. (Ans: 𝐦 = 𝐦 𝟎 ( 𝟏 − 𝐯 𝟐 𝒄 𝟐 ) 𝟏 𝟐 ) 34) Mention Limitations of Dimensional Analysis. [ D.K 2013, D.K 2014] • The constant of proportionality cannot be determined by the method of dimensional analysis. • It cannot be used for relations involving exponential and trigonometry functions. • The method cannot be used to derive equations where addition or subtraction is in volved. Examples s = ut + ½ at 2 and 2as = v 2 – u 2 • If dimensions are given, physical quantity may not be unique as many physical quantities have same dimensions. For example, if the dimensional formula of a physical quantity is [ML 1 T - 2 ] it may be work or energy or torque. • Even though a given equation is dimensionally correct, it’s not possible to conclude that it is truly correct. (e.g., v=u+ at is truly and dimensionally correct whereas v=u+ 2at is dimensionally correct but not truly correct) Problems: 1. Which of the following is the most precise device for measuring length? a) a vernier calipers with 20 divisions on the sliding scale b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale c) an optical instrument that can measure lengt h to within a wavelength of light? (Ans: Option C) ) 2. A student measures the thickness of a human hair by looking at it through a microscope of magnifica- tion 100. He makes 20 observations and finds that the average width of the hair in the field of view of the microscope is 3.5 mm. What is the estimate on the thickness of hair? (Ans: t = 0.035mm) 3. Answer the following: a) You are given a thread and a meter scale. How will you estimate the diameter of the thread? (Ans: 𝐃𝐢𝐚𝐦𝐞𝐭𝐞𝐫 = 𝐋𝐞𝐧𝐠𝐭𝐡 𝐨𝐟 𝐭𝐡𝐞 𝐫𝐨𝐝 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐭𝐮𝐫𝐧𝐬 ) b) A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divi- sions on the circular scale? (Ans: 𝐈𝐭 𝐢𝐬 𝐧𝐨𝐭 𝐩𝐨𝐬𝐬𝐢 𝐛𝐥𝐞 ) c) The mean diameter of a thin brass rod is to be measured by vernier calipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measure- ments only? MCQ QUESTIONS 1) Which of the following systems of units is not based on units of mass, length and time alone? A) SI B) MKS C) CGS D) FPS 2) Number of base SI units is A) 4 B) 7 C) 3 D) 5 3) Second is defined in terms of periods of radiation from Caesium 133 because A) it is not affected by the change of place B) it is not affected by the change of time C) it is not affected by the change of Physical conditions D) All of these. 4) 1° (degree) is equal to A) 17 radian B) 17.45 × 10 – 2 radian C) 17.45 × 10 – 3 radian D) 1.745 × 10 – 2 radian 5) The prototype of the international standard kilogram supplied by the International Bureau of Weights and Measures (BIPM) are available at A) National Physics Laboratory B) National science centre C) CSIR D) None of these 6) Illuminance of a surface is measured in A) lumen B) Candela C) lux D) lux m – 2 7) Universal time is based on A) rotation of the earth on its axis B) earth’s orbital motion around the Sun C) vibrations of caesium atom D) oscillations of quartz crystal 8) What is the correct number of significant figures in 0.0003026? A) Four B) Seven C) Eight D) Six 9) If L = 2. 331 cm, B = 2.1 cm, then L + B = A) 4.4 cm B) 4 cm C) 4.43 cm D) 4.431 cm 10) The area of the triangle ABC is A) 14.5 c m 2 B) 14.490 cm 2 C) 14 cm 2 D) 1.449 cm 2 11) The number of significant figures in 0.00060 m is A) 1 B) 2 C) 3 D) 4 12) The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is A) 6663.821 B) 664 C) 663.8 D) 663.8 13) Number of significant figures in expression (4.327g / 2.51 cm 3 ) is A) 2 B) 4 C) 3 D) 5 14) The dimensions of force are A) [ML 2 T – 1 ] B) [M 2 L 3 T – 2 ] C) [MLT – 2 ] D) None of these 15) The dimensions of speed and velocity are A) [L 2 T], [LT – 1 ] B) [LT – 1 ], [LT – 2 ] C) [LT], [LT] D) [LT – 1 ], [LT – 1 ] 16) Equating a physical quantity with its dimensional formula, is known as A) dimensional analysis B) dimensional equation C) dimensional formula D) none of these 17) Dimensional analysis can be applied to A) check the dimensional consistency of equations B) deduce relations among the physical quantities. C) to convert from one system of units to another D) All of these 18) Two quantities A and B have different dimensions which mathematical operation given below is physically meaningful? A) A/B B) A + B C) A – B D) A = B 19) Which is dimensionless? A) Force/acceleration B) Velocity/acceleration C) Volume/area D) Energy/work 20) Which of the following quantities has a unit but dimensionless? A) Strain B) Reynolds number C) Angular displacement D) Poi sson’s ratio 21) The physical quantity that does not have the dimensional formula [ML – 1 T – 2 ] is A) force B) pressure C) stress D) modulus of elasticity 22) The dimensions of pressure is equal to A) force per unit volume B) energy per unit volume C) force D) energy 23) The dimensional formula of angular velocity is A) [M 1 L 1 T – 1 ] B) [M 0 L 0 T 1 ] C) [M 1 L 0 T – 2 ] D) [M 0 L 0 T – 1 ] 24) For the given figure solid angle, dΩ is equal to A) r 2 dA steradian B) dA/r 2 steradian C) r 2 /dA steradian D) dA/r steradian 25) The solid angle in the following diagram is equal to A) 𝜋 𝑎 2 4 𝑅 2 B) 𝜋 𝑎 2 𝑅 2 C) 𝜋 𝑅 2 𝑎 2 D) 4 𝜋 𝑎 2 𝑅 2 26) The respective number of significant figures for the number 23.023, 0.0003 and 2.1 × 10 – 3 are re- spectively. A) 5, 1 and 2 B) 5, 1 and 5 C) 5, 5 and 2 D) 4, 4 and 2 27) 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 block according to the idea of significant figures should be A) 2 3 1 10 cm B) 2 3 2 10 cm C) 2 3 1.763 10 cm D) None of these 28) The perimeter of a triangle with side AB = 4.331 cm, BC = 6.1 cm, and CA = 3.11 cm A) 13.541 cm B) 13.54 cm C) 13.5 cm D) 13 cm 29) A student has measured length of a wire is equal to 0.04580 m. The value of length has the number of significant figures equal to A) Five B) Four C) Six D) None of these 30) Which of the following is a derived Unit? A) Unit of mass B) Unit of length C) Unit of time D) Unit of volume 31) The symbol to represent “Amount of Substance” is ________ A) K B) A C ) d D) mol 32) Which among the following is the Supplementary Unit —— – A) Mass B) Time C) Solid angle D) Luminosity 33) The sum of the numbers 436.32, 227.2 and 0.301 in appropriate significant figures is A) 6663.821 B) 664 C) 663.8 D) 663.8 34) In SI system the fundamental units are A) meter , kilogram, second, ampere, k elvin, mole and candela B) meter , kilogram, second coulomb, k elvin, mole and candela C) meter , newton, second, ampere, k elvin, mole and candela D) meter , kilogram, second, ampere, elvin, mole and lux 35) There are 20 divisions in 4 cm of the main scale. The vernier scale has 10 divisions. The least count of the instrument is A) 0.05 cm B) 0.5 cm C) 5.0 cm D) 0.005 cm 36) Which of the following is not the name of physical quantity? A) k ilogram B) Density C) Distance D) Energy 37) The value of 0.98 – 0.989 with regard to the significant digit will be: A) 0.001 B) 0.010 × 10 - 1 C) 0.01 × 10 - 1 D) None of these 38) What is the number of significant figures in (3.20 + 4.80) × 10 5 ? A) 2 B) 3 C) 4 D) 5 39) Which of the following numerical values has three significant figures? A) 5.055 B) 0.050 C) 50.50 D) 0.500 40) The magnitude of any physical quantity: A) Depends on the method of measurement B) Does not depend on method of measurement C) Is more in the SI system than in the CGS system D) Is directly proportional to the fundamental units of mass, length and time 41) On the basis of dimensional equation, the maximum number of unknown/s that can be found, is A) one B) two C) three D) four 42) The multiplication of 10.610 with 0.210 up to correct number of significant figures is A) 2.2281 B) 2.228 C) 2.23 D) 2.2 43) The quantity having the same unit in all system of unit is A) mass B) time C) length D) temperature 44) A set of fundamental and derived units is known as A) Base Units B) Fundamental Units C) Sys tem of Units D) None of the above 45) What is the unit of Luminous Intensity? A) Hertz B ) Meters C) Candela D) Kilogram 46) The dimensional formula for the area of the rectangle is A) [M 0 L 2 T 0 ] B ) [M 1 L 2 T 0 ] C) [M 0 L 2 T 1 ] D) [M 1 L 2 T 1 ] 47) The dimensional formula of density is A) [M 1 L - 3 T 0 ] B ) [M 0 L - 3 T 0 ] C) [M 1 L - 3 T 1 ] D) [M 1 L - 1 T 0 ] ANSWER KEYS 1 2 3 4 5 6 7 8 9 10 A B D D A C C A A A 11 12 13 14 15 16 17 18 19 20 B B C C D B D A D C 21 22 23 24 25 26 27 28 29 30 A B D B A A B C B D 31 32 33 34 35 36 37 38 39 40 D C B A D A C B D B 41 42 43 44 45 46 47 C C B B B A A