PHYSICS APPENDIX-A A.1 SI Units SI Base Unit Base Quantity Name Symbol Length metre m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Amount of substance mole mol Luminous intensity candela cd A.2 Some Derived SI Units Quantity Name Symbol Expression in Terms Expression in of Base Units Terms of SI Units Plane angle radian ω m/m Frequency hertz Hz s–1 Force newton N kg · m/s2 J/m Pressure pascal Pa kg/m · s2 N/m2 Energy joule J kg · m2/s2 N · m Power watt W kg · m2/s3 J/s Electric charge coulomb C A · s Electric potential volt V kg · m2/A · s3 W/A Capacitance farad F A2 · s4/kg · m2 C/V Electric resistance ohm Ω kg · m2/A2 · s3 V/A Magnetic flux weber φ kg · m2/A · s2 T· m Magnetic field tesla B kg /A · s2 Nb/m2 or tesla L 2 2 2 2 Inductance henry kg · m /A · s T · m /A APPENDIX-B B.1 Conversion Factors Length m cm km in. ft mi 1 meter 1 102 10–3 39.37 3.281 6.214 × 10–4 1 centimeter 10–2 1 10–5 0.3937 3.281 × 10–2 6.214 × 10–6 1 kilometer 103 105 1 3.937 × 104 3281 × 103 0.6214 1 inch 2.540 × 10–2 2.540 2.540 × 10–5 1 8.333 × 10–2 1.578 × 10–5 1 foot 0.3048 30.48 3.048 × 10–4 12 1 1.894 × 10–4 1 mile 1609 1.609 × 105 1.609 6.336 × 104 5280 1 Mass kg g slug u 1 kilogram 1 103 6.854 × 10–2 6.024 × 1026 1 gram 10–3 1 6.852 × 10–5 6.024 × 1023 1 slug 14.59 1.459 × 104 1 8.789 × 1027 1 atomic mass unit 1.660 × 10–27 1.660 × 10–24 1.137 × 10–28 1 Note : 1 metric ton = 1000 kg. 2 Oswaal JEE (Main) Mock Test 15 Sample Question Papers Time s min h day yr 1 second 1 1.667 × 10–2 2.778 × 10–4 1.157 × 10–5 3.169×10–8 1 minute 60 1 1.667 × 10–2 6.944 × 10–4 1.901×10–6 1 hour 3600 60 1 4.167×10–2 1.141×10–4 1 day 8.640 × 104 1440 24 1 2.738×10–5 1 year 3.156 × 107 5.259 × 105 8.766 × 103 365.2 1 Speed m/s cm/s ft/s mi/h 1 meter per second 1 102 3.281 2.237 1 centimeter per second 10–2 1 3.281 ×10–2 2.237 ×10–2 1 foot per second 0.3048 30.48 1 0.6818 1 mile per hour 0.4470 44.70 1.467 1 Note : 1 mi/min = 60 mi/h = 88 ft/s. Force N lb 1 newton 1 0.2248 1 pound 4.448 1 Energy, Energy Transfer J ft · lb eV 1 joule 1 0.7376 6.242 × 1018 1 foot-pound 1.356 1 8.464 × 1018 1 electron volt 1.602 × 10–19 1.182 × 10–19 1 1 calorie 4.186 3.087 2.613 × 1019 1 British thermal unit 1.055 × 103 7.779 × 102 6.585 × 1021 1 kilowatt-hour 3.600 × 106 2.655 × 106 2.247 × 1025 cal Btu kWh 1 joule 0.2389 9.481 × 10–4 2.778 × 10–7 1 foot-pound 0.3239 1.285 × 10–3 3.766 × 10–7 1 electron volt 3.827 × 10–20 1.519 × 10–22 4.450 × 10–26 1 calorie 1 3.968 × 10–3 1.163 × 10–6 1 British thermal unit 2.520 × 102 1 2.930 × 10–4 1 kilowatt-hour 8.601 × 105 3.413 × 102 1 Pressure Pa atm 1 pascal 1 9.869 × 10–6 1 atmosphere 1.013 × 105 1 1 centimeter mercurya 1.333 × 103 1.316 × 10–2 1 pound per square inch 6.895 × 103 6.805 × 10–2 1 pound per square foot 47.88 4.725 × 10–4 cm Hg lb/in.2 lb/ft2 1 pascal 7.501 × 10–4 1.450 × 10–4 2.089 × 10–2 1 atmosphere 76 14.70 2.116 × 103 1 centimeter mercurya 1 0.1943 27.85 1 pound per square inch 5.171 1 144 1 pound per square foot 3.591 × 10–2 6.944 × 10–3 1 At 0°C and at a location where the free-fall acceleration has its “standard” value, 9.80665 m/s2. Appendix (Physics) 3 B.2 Conversions of useful physical quantities Length Acceleration 1 in. = 2.54 cm (exact) 1 m/s2 = 3.28 ft/s2 = 100 cm/s2 1 m = 39.37 in. = 3.281 ft 1 ft/s2 = 0.3048 m/s2 = 30.48 cm/s2 1 ft = 0.3048 m Pressure 12 in. = 1 ft 5 2 2 3 ft = 1 yd 1 bar = 10 N/m = 14.50 lb/in. 1 yd = 0.9144 m 1 atm = 760 mm Hg = 76.0 cm Hg 1 km = 0.621 mi 1 atm = 14.7 lb/in.2 = 1.013 × 105 N/m2 1 mi = 1.609 km 1 Pa = 1 N/m2 = 1.45 × 10–4 lb/in.2 1 mi = 5280 ft Time 1 μm = 10–6 m = 103 nm 1 light-year = 9.461 × 1015 m 1 yr = 365 days = 3.16 × 107 s Area 1 day = 24 h = 1.44 × 103 min = 8.64 × 104 s 1 m2 = 104 cm2 = 10.76 ft2 Energy 2 2 2 1 ft = 0.0929 m = 144 in. 1 J = 0.738 ft · lb 1 in.2 = 6.452 cm2 1 cal = 4.186 J Volume 1 Btu = 252 cal = 1.054 × 103 J 1 m3 = 106 cm3 = 6.102 × 104 in.3 1 eV = 1.602 × 10–19 J 1 ft3 = 1 728 in.3 = 2.83 × 10–2 m3 6 1 L = 1000 cm3 = 1.0576 qt = 0.0353 ft3 1 kWh = 3.60 × 10 J 1 ft3 = 7.481 gal = 28.32 L = 2.832 × 10–2 m3 Power 3 1 gal = 3.786 L = 231 in. 1 hp = 550 ft · lb/s = 0.746 kW Mass 1 W = 1 J/s = 0.738 ft · lb/s 1000 kg = 1 t (metric ton) 1 Btu/h = 0.293 W 1 slug = 14.59 kg Some Approx imations Useful for Estimation 1 u = 1.66 × 10–27 kg = 931.5 MeV/c2 Problems Force 1 m ≈ 1 yd 1 m/s ≈ 2 mi/h 1 N = 0.2248 lb 7 1 lb = 4.448 N 1 kg ≈ 2 lb 1 yr ≈ π × 10 s 1 Velocity 1 N ≈ lb 60 mi/h ≈ 100 ft/s 1 mi/h = 1.47 ft/s = 0.447 m/s = 1.61 km/h 4 1 1 1 m/s = 100 cm/s = 3.281 ft/s 1 L ≈ gal 1 km ≈ mi 4 2 1 mi/min = 60 mi/h = 88 ft/s APPENDIX-C C.1 Important Constants Symbol Meaning Best Value Approximate Value c Speed of light in vacuum 2.99792458 × 108 m/s 3.00 × 108 m/s G Gravitational constant 6.67408(31) × 10–11 N . m2 /kg2 6.67 × 10–11 N . m2 /kg2 23 23 NA Avogadro’s number 6.02214129(27) × 10 6.02 × 10 k Boltzmann’s constant 1.3806488(13) × 10–23 J/K 1.38 × 10–23 J/K 8.31 J/ mol · K = 1.99 cal / mol . K R Gas constant 8.3144621(75) J/ mol . K = 0.0821 atm . L/mol . K s Stefan-Boltzmann constant 5.670373(21) × 10–8 W/m2 . K 5.67 × 10–8 W/m2 · K k Coulomb force constant 8.987551788… × 109 N . m2/ C2 8.99 × 109 N . m2/ C2 –19 –19 qe Charge on electron –1.602176565(35) × 10 C –1.60 × 10 C –12 2 2 –12 2 2 ε0 Permittivity of free space 8.854187817… × 10 C /N . m 8.85 × 10 C /N . m –7 –6 µ0 Permeability of free space 4π × 10 T . m/A 1.26 × 10 T . m/A h Planck’s constant 6.62606957(29) × 10–34 J . s 6.63 × 10–34 J . s 4 Oswaal JEE (Main) Mock Test 15 Sample Question Papers C.2 Submicroscopic Masses Symbol Meaning Best Value Approximate Value –31 –31 me Electron mass 9.10938291(40) × 10 kg 9.11 × 10 kg –27 –27 mp Proton mass 1.672621777(74) × 10 kg 1.6726 × 10 kg –27 –27 mn Neutron mass 1.674927351(74) × 10 kg 1.6749 × 10 kg u Atomic mass unit 1.660538921(73) × 10–27 kg 1.6605 × 10–27 kg C.3 Solar System Data Sun mass 1.99 × 1030 kg average radius 6.96 × 108 m Earth-sun distance (average) 1.496 × 1011 m Earth mass 5.9736 × 1024 kg average radius 6.376 × 106 m orbital period 3.16 × 107 s Moon mass 7.35 × 1022 kg average radius 1.74 × 106 m orbital period (average) 2.36 × 106 s Earth-moon distance (average) 3.84 × 108 m C.4 Metric Prefixes for Powers of Ten and Their Symbols Prefix Symbol Value Prefix Symbol Value tera T 1012 deci d 10–1 giga G 109 centi c 10–2 mega M 106 milli m 10–3 kilo k 103 micro µ 10–6 hecto h 102 nano n 10–9 deka da 101 pico p 10–12 – – 100 ( = 1 ) femto f 10–15 –28 2 C.5 Selected British Units 1 barn (b) = 10 m Volume 1 liter (L) = 10–3 m3 Length 1 inch (in.) = 2.54 cm (exactly) 1 U.S.