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PHYSICS FORMULAS FOR CLASS IX prepared by SIR ABID

The document lists various physics formulas relevant for students in class IX, covering topics such as volume of geometric shapes, laws of motion, forces, and energy. Each formula is presented with its corresponding variables and physical quantities. The document serves as a comprehensive reference for mathematical concepts in physics, especially focusing on calculations involving different physical phenomena.

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GBSS NO.3 SHAH FAISAL COLONY NO.4, KARACHI 1 ‫ومےل‬‫افر‬‫ےک‬‫زفسک‬ ‫(ونںی‬ ‫ےئل‬‫ےک‬‫الس‬‫ک‬ ) ‫اعدب‬‫دمحم‬ )‫زفسک‬‫الڈیئ‬‫پ‬‫سی۔یس(ا‬‫می۔ا‬‫ا‬ ‫ڈ‬‫پ‬‫یب۔ا‬ ‫وکسل‬‫ا‬‫ی‬‫دنکیسر‬‫ز‬‫ئ‬‫وبا‬‫ٹنمن‬‫وگر‬ ‫ربمن‬ ۳ ‫ربمن‬‫اکولین‬‫لصیف‬‫ہ‬‫ا‬‫ش‬ ۴ ‫یچ‬‫رکا‬،
GBSS NO.3 SHAH FAISAL COLONY NO.4, KARACHI 2 PHYSICS FORMULAS FOR CLASS IX S. No. Formula Symbol Physical Quantity 1 𝑉 = 4 3 𝜋𝑟3 𝑉 Volume of sphere(ball) ( )‫مجح‬‫اک‬‫دنیگ‬‫ینعی‬‫ّہ‬‫رک‬ 𝜋 pi )‫(اپیئ‬ r radius of sphere )‫رطق‬‫فصن‬‫اک‬‫دنیگ‬‫ینعی‬‫ّے‬‫رک‬( 2 𝜌 = 𝑚 𝑉 or 𝑚 = 𝜌𝑉 𝜌 density )‫(اثکتف‬ 𝑚 mass )‫(تیمک‬ 𝑉 Volume )‫(مجح‬ 3 𝐴 = 𝜋𝑟2 𝐴 Area of the cylinder ‫ل‬‫ی‬‫س‬( )‫رہبق‬‫اک‬‫ر‬‫ڈ‬‫ی‬ 𝜋 pi )‫(اپیئ‬ r radius of the cylinder ‫ل‬‫ی‬‫س‬( )‫رطق‬‫فصن‬‫اک‬‫ر‬‫ڈ‬‫ی‬ 4 𝑉 = 𝑙3 𝑉 Volume of cube )‫مجح‬‫اک‬‫(بعکم‬ 𝑙 length of each side )‫ابملیئ‬‫یک‬‫علض‬‫(رہ‬ 5 𝑉 = 𝜋𝑟2 ℎ 𝑉 Volume of cylinder ‫اک‬‫ر‬‫ڈ‬‫ی‬‫ل‬‫ی‬‫س‬( )‫مجح‬ 𝜋 pi )‫(اپیئ‬ r radius of the cylinder )‫رطق‬‫فصن‬‫اک‬‫ر‬‫ڈ‬‫ی‬‫ل‬‫ی‬‫س‬( ℎ height or length of cylinder )‫ابملیئ‬‫ای‬‫اواچنیئ‬‫یک‬‫ر‬‫ڈ‬‫ی‬‫ل‬‫ی‬‫س‬( 6 𝑉 = 1 3 𝑙2 ℎ 𝑉 Volume of pyramid )‫مجح‬‫اک‬‫(رخموط‬ 𝑙 length of each side of base )‫ابملیئ‬‫یک‬‫علض‬‫رہ‬‫ےک‬‫(اقدعہ‬ ℎ height or length of pyramid )‫ابملیئ‬‫ای‬‫اواچنیئ‬‫یک‬‫(رخموط‬ 7 𝑣 = 𝑆 𝑡 𝑣 average speed (‫راتفر‬‫)اوطس‬ 𝑆 distance (‫)افہلص‬ 𝑡 time (‫)وتق‬ 8 𝑎 = 𝑣𝑓 − 𝑣𝑖 𝑡 or 𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡 𝑣𝑓 final velocity (‫والیٹس‬‫)آرخی‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 𝑎 acceleration (‫)ارساع‬ 𝑡 time (‫)وتق‬ 9 𝑆 = 𝑣𝑖𝑡 + 1 2 𝑎𝑡2 𝑆 distance (‫)افہلص‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 𝑡 time (‫)وتق‬ 𝑎 acceleration (‫)ارساع‬
GBSS NO.3 SHAH FAISAL COLONY NO.4, KARACHI 3 10 2𝑎𝑆 = 𝑣𝑓 2 − 𝑣𝑖 2 𝑎 acceleration (‫)ارساع‬ 𝑆 distance (‫)افہلص‬ 𝑣𝑓 final velocity (‫والیٹس‬‫)آرخی‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 11 𝑣𝑓 = 𝑣𝑖 + 𝑔𝑡 𝑣𝑓 final velocity (‫والیٹس‬‫)آرخی‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝑡 time (‫)وتق‬ 12 ℎ = 𝑣𝑖𝑡 + 1 2 𝑔𝑡2 ℎ height (‫)دنلبی‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 𝑡 time (‫)وتق‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 13 2𝑔ℎ = 𝑣𝑓 2 − 𝑣𝑖 2 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) ℎ height (‫)دنلبی‬ 𝑣𝑓 final velocity (‫والیٹس‬‫)آرخی‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 14 𝐹 = 𝑚𝑎 𝐹 Force (‫)وقت‬ 𝑚 mass (‫)تیمک‬ 𝑎 acceleration (‫)ارساع‬ 15 𝑊 = 𝑚𝑔 𝑊 Weight (‫)وزن‬ 𝑚 mass (‫)تیمک‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 16 𝑝 = 𝑚𝑣 𝑝 Momentum (‫م‬ ‫ٹ‬‫ن‬‫ی‬‫م‬ ‫)وم‬ 𝑚 mass (‫)تیمک‬ 𝑣 speed (‫)راتفر‬ 17 𝐹 = 𝑝𝑓 − 𝑝𝑖 𝑡 𝐹 Force (‫)وقت‬ 𝑝𝑓 final momentum )‫م‬ ‫ٹ‬‫ن‬‫ی‬‫م‬ ‫وم‬‫(آرخی‬ 𝑝𝑖 Initial momentum )‫م‬ ‫ٹ‬‫ن‬‫ی‬‫م‬ ‫وم‬‫(ادتبایئ‬ 𝑡 time )‫(وتق‬
GBSS NO.3 SHAH FAISAL COLONY NO.4, KARACHI 4 18 𝑚1𝑢1 + 𝑚2𝑢2 = 𝑚1𝑣1 + 𝑚2𝑣2 𝑚1 mass of the first body (‫تیمک‬‫یک‬‫مسج‬‫)ےلہپ‬ 𝑢1 speed of first body before collision (fire) ‫راتفر‬‫یک‬‫مسج‬‫ےلہپ‬،‫ےلہپ‬‫ےس‬)‫(افرئ‬‫رکٹاےن‬ 𝑚2 mass of the second body (‫تیمک‬‫یک‬‫مسج‬‫)دورسے‬ 𝑢2 speed of second body before collision (fire) ‫راتفر‬‫یک‬‫مسج‬‫دورسے‬،‫ےلہپ‬‫ےس‬)‫(افرئ‬‫رکٹاےن‬ 𝑣1 speed of first body after collision (fire) ‫راتفر‬‫یک‬‫مسج‬‫ےلہپ‬،‫دعب‬‫ےک‬)‫(افرئ‬‫رکٹاےن‬ 𝑣2 speed of second body after collision (fire) ‫راتفر‬‫یک‬‫مسج‬‫دورسے‬،‫دعب‬‫ےک‬)‫(افرئ‬‫رکٹاےن‬ 19 𝐹 𝑠 = 𝜇𝑅 𝐹 𝑠 Force of friction (‫وقت‬‫یک‬‫)رڑگ‬ 𝜇 Coefficient of friction (‫رشح‬‫یک‬‫)رڑگ‬ 𝑅 Normal reaction ( ‫ومعدی‬ ‫لمع‬ِّّ‫د‬‫ر‬ ) 20 𝑅 = 𝑊 or 𝑅 = 𝑚𝑔 𝑅 Normal reaction (‫لمع‬ِّّ‫د‬‫ر‬‫)ومعدی‬ 𝑊 Weight (‫)وزن‬ 𝑚 mass (‫)تیمک‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 21 𝑎𝑐 = 𝑣2 𝑟 𝑎𝑐 Centripetal acceleration (‫ارساع‬‫املئ‬‫)رمزک‬ 𝑣 speed (‫)راتفر‬ 𝑟 radius (‫رطق‬‫)فصن‬ 22 𝐹 𝑐 = 𝑚𝑣2 𝑟 𝐹 𝑐 Centripetal Force (‫وقت‬‫املئ‬‫)رمزک‬ 𝑚 mass (‫)تیمک‬ 𝑣 speed (‫)راتفر‬ 𝑟 radius (‫رطق‬‫)فصن‬ 23 𝐹 𝑥 = 𝐹 𝑐𝑜𝑠 𝜃 𝐹 𝑥 horizontal or x component (‫زج‬ -x) 𝐹 Force (‫)وقت‬ 𝜃 angle (‫)زاوہی‬ 24 𝐹 𝑦 = 𝐹 𝑠𝑖𝑛 𝜃 𝐹 𝑦 vertical or y component (‫زج‬ -y) 𝐹 Force (‫)وقت‬ 𝜃 angle (‫)زاوہی‬ 25 𝐹 = √𝐹 𝑥 2 + 𝐹 𝑦 2 𝐹 magnitude of 𝐹 ⃗ (‫تمیق‬‫دعدی‬‫یک‬ 𝐹 ⃗) 𝐹 𝑥 horizontal or x component (‫زج‬ -x) 𝐹 𝑦 vertical or y component (‫زج‬ -y)
GBSS NO.3 SHAH FAISAL COLONY NO.4, KARACHI 5 26 𝜃 = tan−1 𝐹 𝑦 𝐹 𝑥 𝜃 direction of 𝐹 ⃗ ( ‫یک‬ ‫تمس‬ 𝐹 ⃗) 𝐹 𝑦 vertical or y component (‫زج‬ -y) 𝐹 𝑥 horizontal or x component (‫زج‬ -x) 27 𝜏 = 𝐹 × 𝑑 Or 𝜏 = 𝐹 × 𝐿 𝜏 torque (‫)اٹرک‬ 𝐹 Force (‫)وقت‬ 𝑑 or L Length of moment arm ( ‫آرم‬‫ومٹنم‬ ‫ابملیئ‬‫یک‬ ) 28 𝜏 = 𝐹 × 𝑑 𝜏 moment of couple or Torque ( ‫اک‬‫لپک‬ ‫اٹرک‬ ) 𝐹 Force (‫)وقت‬ 𝑑 length of the moment arm of the couple )‫آرم‬‫(لپک‬ 29 Clockwise moments = anticlockwise moments 𝐹1 × 𝑑1 = 𝐹2 × 𝑑2 𝐹1 1st Force or weight )‫وزن‬‫ای‬‫وقت‬‫(یلہپ‬ 𝑑1 Moment arm of 𝐹1)‫آرم‬‫ومٹنم‬‫اک‬ ‫وقت‬‫(یلہپ‬ 𝐹2 2nd Force or weight )‫وزن‬‫ای‬‫وقت‬‫(دورسی‬ 𝑑2 Moment arm of 𝐹2 )‫آرم‬‫ومٹنم‬‫اک‬‫وقت‬‫(دورسی‬ 30 First condition of equilibrium ∑ 𝐹 𝑥 = 0 , ∑ 𝐹 𝑦 = 0 ∑ 𝐹 = 0 ∑ 𝐹 𝑥 Sum of x components of Forces ( ‫ا‬ ‫زج‬ ‫ومجمہع‬‫اک‬‫ا‬ -x ‫وقوت‬ ‫ےک‬‫ں‬ ) ∑ 𝐹 𝑦 Sum of y components of Forces )‫ومجمہع‬‫اک‬‫ازجا‬ -y ‫وقوت‬ ‫ں‬ ‫ےک‬ ) ∑ 𝐹 Sum of all Forces )‫ومجمہع‬‫اک‬‫وقوتں‬‫(امتم‬ 31 Second condition of equilibrium ∑ 𝜏 = 0 ∑ 𝜏 Sum of all torques (‫ومجمہع‬‫اک‬‫اٹروکں‬‫)امتم‬ 32 𝑃 = 𝐹 𝐴 𝑃 Pressure )‫(دابؤ‬ 𝐹 Force )‫(وقت‬ 𝐴 Area )‫(رہبق‬ 33 𝑃 = 𝑑𝜌𝑔 𝑃 Pressure )‫(دابؤ‬ 𝑑 depth )‫(رہگایئ‬ 𝜌 Density )‫(اثکتف‬ 𝑔 Acceleration due to gravity )‫ارساع‬‫ی‬‫قل‬‫ث‬( 34 𝐹 = 𝐾𝑥 𝐹 Force (‫)وقت‬ 𝐾 spring constant (‫لقتسم‬‫اک‬‫)ارپسگن‬ 𝑥 Extension (‫اچنھکؤ‬‫ای‬‫)ڑباھؤ‬
GBSS NO.3 SHAH FAISAL COLONY NO.4, KARACHI 6 35 𝐹 = 𝐺 𝑚1𝑚2 𝑟2 𝐹 Force of gravitation (‫وقت‬‫)اجتذیب‬ 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝑚1 mass of the first body (‫تیمک‬‫یک‬‫مسج‬‫)ےلہپ‬ 𝑚2 mass of the second body (‫تیمک‬‫یک‬‫مسج‬‫)دورسے‬ 𝑟 distance (‫)افہلص‬ 36 𝑀𝑒 = 𝑔𝑅𝑒 2 𝐺 𝑀𝑒 Mass of earth (‫تیمک‬‫یک‬‫)زنیم‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝑅𝑒 Radius of earth (‫رطق‬‫فصن‬‫اک‬‫)زنیم‬ 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 37 𝑀𝑝 = 𝑔𝑅𝑝 2 𝐺 𝑀𝑝 Mass of planet ( ‫ارے‬ ّ‫س‬ ‫تیمک‬‫یک‬ ) 𝑔 acceleration due to gravity on planet (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝑅𝑝 Radius of planet ( ‫ارے‬ ّ‫س‬ ‫رطق‬‫فصن‬‫اک‬ ) 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 38 𝑔𝑒 = 𝐺𝑀𝑒 𝑅𝑒 2 𝑔𝑒 acceleration due to gravity on earth (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝑀𝑒 Mass of earth (‫تیمک‬‫یک‬‫)زنیم‬ 𝑅𝑒 Radius of earth (‫رطق‬‫فصن‬‫اک‬‫)زنیم‬ 39 𝑔𝑝 = 𝐺𝑀𝑝 𝑅𝑝 2 𝑔𝑝 acceleration due to gravity on planet (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝑀𝑝 Mass of planet ( ‫ارے‬ ّ‫س‬ ‫تیمک‬‫یک‬ ) 𝑅𝑝 Radius of planet ( ‫ارے‬ ّ‫س‬ ‫رطق‬‫فصن‬‫اک‬ ) 40 𝑣 = √ 𝐺𝑀 𝑅 + ℎ 𝑣 Speed of satellite ‫(ونصمیع‬ )‫راتفر‬‫یک‬‫ارے‬ ّ‫س‬ 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝑀 Mass of planet(earth) ( ‫ارے‬ ّ‫س‬ ‫تیمک‬‫یک‬ ) 𝑅 Radius of planet(earth) ( ‫ارے‬ ّ‫س‬ ‫رطق‬‫فصن‬‫اک‬ ) ℎ height(altitude) of satellite )‫(دنلبی‬ 41 𝑣𝑐 = √𝑔𝑅 𝑣𝑐 Critical velocity of satellite ‫(ونصمیع‬ )‫والیٹس‬‫افلص‬‫یک‬‫ارے‬ ّ‫س‬ 𝑔 Acceleration due to gravity )‫ارساع‬‫ی‬‫قل‬‫ث‬( 𝑅 Radius of planet(earth) ( ‫ارے‬ ّ‫س‬ ‫رطق‬‫فصن‬‫اک‬ ) 42 𝑃1𝑉1 = 𝑃2𝑉2 𝑃1 Initial Pressure (‫دابؤ‬‫)ادتبایئ‬ 𝑉1 Initial Volume (‫مجح‬‫)ادتبایئ‬ 𝑃2 Final Pressure (‫دابؤ‬‫)آرخی‬ 𝑉2 Final Volume (‫مجح‬‫)آرخی‬
GBSS NO.3 SHAH FAISAL COLONY NO.4, KARACHI 7 43 𝑊 = 𝐹. 𝑑 or 𝑊 = 𝐹𝑑 𝑐𝑜𝑠 𝑐𝑜𝑠 𝜃 𝑊 Work done (‫)اکم‬ 𝐹 Force (‫)وقت‬ 𝑑 Displacement (‫)اٹہؤ‬ 𝜃 angle (‫)زاوہی‬ 44 𝑃 = 𝑊 𝑡 𝑃 Power (‫)اطتق‬ 𝑊 Work done (‫)اکم‬ 𝑡 time (‫)وتق‬ 45 𝐾. 𝐸 = 1 2 𝑚𝑣2 𝐾. 𝐸 Kinetic Energy (‫وتاانیئ‬‫)رحیک‬ 𝑚 mass (‫)تیمک‬ 𝑣 velocity (‫)والیٹس‬ 46 𝑃. 𝐸 = 𝑚𝑔ℎ 𝑃. 𝐸 Potential Energy (‫وتاانیئ‬‫ل‬‫ش‬‫ن‬‫ی‬‫ٹ‬ ‫وپ‬‫ای‬‫)یفخم‬ 𝑚 mass (‫)تیمک‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) ℎ height (‫)دنلبی‬ 47 Ƞ = 𝐸2 𝐸1 × 100 Ƞ Efficiency )‫(اکررکدیگ‬ 𝐸2 Energy as output )‫وتاانیئ‬‫ٹپ‬‫(آؤٹ‬ 𝐸1 Energy as input )‫وتاانیئ‬‫ٹپ‬‫(ان‬ 48 ℉ = 1.8℃ + 32 ℉ Temperature in Fahrenheit ( ‫رحات‬ٔ‫ہج‬‫در‬ ‫اہٹیئ‬‫افرن‬ ‫ںیم‬ ) ℃ Temperature in Celsius ( ‫ی‬‫س‬ ‫رحات‬ٔ‫ہج‬‫در‬ ‫س‬‫شن‬‫ل‬ ‫ںیم‬ ) 49 𝐾 = ℃ + 273 𝐾 Temperature in Kelvin (‫ںیم‬‫ولیکن‬‫رحارت‬ٔ‫ہج‬‫)در‬ ℃ Temperature in Celsius ( ‫ی‬‫س‬ ‫رحات‬ٔ‫ہج‬‫در‬ ‫س‬‫شن‬‫ل‬ ‫ںیم‬ ) 50 ∆𝐿 = 𝛼L∆𝑇 ∆𝐿 change or increase in Length ( ‫ںیم‬‫ابملیئ‬ ‫ای‬‫دبتیلی‬ ‫ااضہف‬ ) 𝛼 Coefficient of linear expansion (‫رشح‬‫یک‬‫الیھپؤ‬‫)وطیل‬ L Initial or original Length (‫ابملیئ‬‫)ادتبایئ‬ ∆𝑇 change in Temperature ( ‫رحارت‬‫درہج‬ ‫ںیم‬ ‫ای‬‫دبتیلی‬ ‫ااضہف‬ ) 51 ∆𝑉 = 𝛽𝑉∆𝑇 ∆𝑉 change or increase in Volume ( ‫مجح‬ ‫ںیم‬ ‫ای‬‫دبتیلی‬ ‫ااضہف‬ ) 𝛽 Coefficient of volumetric expansion ( ‫ی‬‫م‬‫ج‬‫ح‬ ‫رشح‬‫یک‬‫الیھپؤ‬ ) 𝑉 Initial or original Volume ( ‫ادتبایئ‬ ‫مجح‬ ) ∆𝑇 change in Temperature ( ‫رحارت‬‫درہج‬ ‫ںیم‬ ‫ای‬‫دبتیلی‬ ‫ااضہف‬ ) 52 𝛽 = 3𝛼 𝛽 Coefficient of volumetric expansion (‫رشح‬‫یک‬‫الیھپؤ‬‫ی‬‫م‬‫ج‬‫ح‬ ) 𝛼 Coefficient of linear expansion (‫رشح‬‫یک‬‫الیھپؤ‬‫)وطیل‬
GBSS NO.3 SHAH FAISAL COLONY NO.4, KARACHI 8 53 𝑐 = ∆𝑄 𝑚∆𝑇 𝑐 Specific heat capacity )‫وصخمہص‬ ِّ ‫(رحارت‬ ∆𝑄 Amount of heat )‫دقمار‬‫یک‬‫(رحارت‬ 𝑚 mass )‫(تیمک‬ ∆𝑇 Change in Temperature )‫دبتیلی‬‫ںیم‬‫رحارت‬‫(درہج‬ Some important values for numericals Quantity Symbol Value Acceleration due to gravity )‫ارساع‬‫ی‬‫قل‬‫ث‬( 𝑔 10 ms-2 (approximately) Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝐺 6.673 x 10-11 Nm2kg-2 Radius of earth (‫رطق‬‫فصن‬‫اک‬‫)زنیم‬ 𝑅𝑒 6.38 x 106 m Mass of earth (‫تیمک‬‫یک‬‫)زنیم‬ 𝑀𝑒 6.0 x 1024 kg Specific heat capacity of water )‫وصخمہص‬ ِّ ‫رحارت‬‫یک‬‫(اپین‬ 𝑐 4200 Jkg-1 oc-1 Specific heat capacity of copper )‫وصخمہص‬ ِّ ‫رحارت‬‫یک‬‫(اتہبن‬ 𝑐 385 Jkg-1 oc-1
GBSS NO.3 SHAH FAISAL COLONY NO.4, KARACHI 9 Some Units of Physical Quantities For Numericals Quantity Quantity Symbol Unit Unit Symbol Length )‫(ابملیئ‬ L meter ‫(رٹیم‬ ) m Temperature )‫رحارت‬‫(درہج‬ T Kelvin )‫(ولیکن‬ K Electric current )‫رکٹن‬‫(ربیق‬ I Ampere )‫ر‬‫ی‬‫ی‬‫من‬‫ی‬ ‫(ا‬ A mass )‫(تیمک‬ 𝑚 kilogram )‫(ولکرگام‬ kg time (‫)وتق‬ 𝑡 second )‫(ڈنکیس‬ s amount of substance )‫دقمار‬‫یک‬‫(ےش‬ n mole )‫(ومل‬ mol Luminous intensity ‫دش‬‫یک‬‫(روینش‬ )‫ت‬ 𝐼𝑣 candela )‫(ڈنیکالی‬ cd Volume ( )‫مجح‬ 𝑉 cubic meter )‫رٹیم‬‫(بعکم‬ m3 Energy )‫(وتاانیئ‬ 𝐸 Joule )‫(وجل‬ J radius ( )‫رطق‬‫فصن‬ r meter ‫(رٹیم‬ ) m density )‫(اثکتف‬ 𝜌 kilogram per cubic meter )‫رٹیم‬‫بعکم‬‫یف‬‫(ولکرگام‬ kg/m3 speed (‫)راتفر‬ 𝑣 meter per second )‫ڈنکیس‬‫یف‬‫(رٹیم‬ ms-1 distance (‫)افہلص‬ 𝑆 or d meter ‫(رٹیم‬ ) m Area ( )‫رہبق‬ 𝐴 meter square )‫رٹیم‬‫(رمعب‬ m2 acceleration (‫)ارساع‬ 𝑎 meter per second square )‫ڈنکیس‬‫رمعب‬‫یف‬‫(رٹیم‬ ms-2 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝑔 meter per second square )‫ڈنکیس‬‫رمعب‬‫یف‬‫(رٹیم‬ ms-2 height (‫)دنلبی‬ ℎ meter ‫(رٹیم‬ ) m Force (‫)وقت‬ 𝐹 Newton )‫(ویننٹ‬ N Weight (‫)وزن‬ 𝑊 Newton )‫(ویننٹ‬ N Momentum (‫م‬ ‫ٹ‬‫ن‬‫ی‬‫م‬ ‫)وم‬ 𝑝 kilogram meter per second )‫ڈنکیس‬‫یف‬‫رٹیم‬‫(ولکرگام‬ kgm/s Normal reaction (‫لمع‬ِّّ‫د‬‫ر‬‫)ومعدی‬ 𝑅 Newton )‫(ویننٹ‬ N torque (‫)اٹرک‬ 𝜏 Newton meter )‫رٹیم‬‫(ویننٹ‬ Nm Pressure )‫(دابؤ‬ 𝑃 Pascal )‫(اپلکس‬ Pa depth )‫(رہگایئ‬ 𝑑 meter ‫(رٹیم‬ ) m Extension (‫اچنھکؤ‬‫ای‬‫)ڑباھؤ‬ 𝑥 meter ‫(رٹیم‬ ) m Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝐺 Newton meter square per kilogram square )‫ولکرگام‬‫رمعب‬‫یف‬‫رٹیم‬‫رمعب‬‫(ویننٹ‬ Nm2kg-2 Work done (‫)اکم‬ 𝑊 Joule )‫(وجل‬ J displacement (‫)اٹہؤ‬ 𝑑 meter ‫(رٹیم‬ ) m
GBSS NO.3 SHAH FAISAL COLONY NO.4, KARACHI 10 Power (‫)اطتق‬ 𝑃 watt )‫(واٹ‬ w Kinetic Energy (‫وتاانیئ‬‫)رحیک‬ 𝐾. 𝐸 Joule )‫(وجل‬ J velocity (‫)والیٹس‬ 𝑣 meter per second )‫ڈنکیس‬‫یف‬‫(رٹیم‬ ms-1 Potential Energy (‫وتاانیئ‬‫ل‬‫ش‬‫ن‬‫ی‬‫ٹ‬ ‫وپ‬‫ای‬‫)یفخم‬ 𝑃. 𝐸 Joule )‫(وجل‬ J Coefficient of linear expansion (‫رشح‬‫یک‬‫الیھپؤ‬‫)وطیل‬ 𝛼 per degree Celsius )‫س‬‫شن‬‫ل‬‫ی‬‫س‬ ‫ڈرگی‬‫(یف‬ oc-1 Coefficient of volumetric expansion ( ‫ی‬‫م‬‫ج‬‫ح‬ ‫رشح‬‫یک‬‫الیھپؤ‬ ) 𝛽 per degree Celsius )‫س‬‫شن‬‫ل‬‫ی‬‫س‬ ‫ڈرگی‬‫(یف‬ oc-1 Specific heat capacity )‫وصخمہص‬ ِّ ‫(رحارت‬ 𝑐 Joule per kilogram per degree Celsius )‫س‬‫شن‬‫ل‬‫ی‬‫س‬ ‫ڈرگی‬‫یف‬‫ولکرگام‬‫یف‬‫(وجل‬ J/kgoc-1 Amount of heat )‫دقمار‬‫یک‬‫(رحارت‬ ∆𝑄 Joule )‫(وجل‬ J

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PHYSICS FORMULAS FOR CLASS IX prepared by SIR ABID

  • 1.
    GBSS NO.3 SHAHFAISAL COLONY NO.4, KARACHI 1 ‫ومےل‬‫افر‬‫ےک‬‫زفسک‬ ‫(ونںی‬ ‫ےئل‬‫ےک‬‫الس‬‫ک‬ ) ‫اعدب‬‫دمحم‬ )‫زفسک‬‫الڈیئ‬‫پ‬‫سی۔یس(ا‬‫می۔ا‬‫ا‬ ‫ڈ‬‫پ‬‫یب۔ا‬ ‫وکسل‬‫ا‬‫ی‬‫دنکیسر‬‫ز‬‫ئ‬‫وبا‬‫ٹنمن‬‫وگر‬ ‫ربمن‬ ۳ ‫ربمن‬‫اکولین‬‫لصیف‬‫ہ‬‫ا‬‫ش‬ ۴ ‫یچ‬‫رکا‬،
  • 2.
    GBSS NO.3 SHAHFAISAL COLONY NO.4, KARACHI 2 PHYSICS FORMULAS FOR CLASS IX S. No. Formula Symbol Physical Quantity 1 𝑉 = 4 3 𝜋𝑟3 𝑉 Volume of sphere(ball) ( )‫مجح‬‫اک‬‫دنیگ‬‫ینعی‬‫ّہ‬‫رک‬ 𝜋 pi )‫(اپیئ‬ r radius of sphere )‫رطق‬‫فصن‬‫اک‬‫دنیگ‬‫ینعی‬‫ّے‬‫رک‬( 2 𝜌 = 𝑚 𝑉 or 𝑚 = 𝜌𝑉 𝜌 density )‫(اثکتف‬ 𝑚 mass )‫(تیمک‬ 𝑉 Volume )‫(مجح‬ 3 𝐴 = 𝜋𝑟2 𝐴 Area of the cylinder ‫ل‬‫ی‬‫س‬( )‫رہبق‬‫اک‬‫ر‬‫ڈ‬‫ی‬ 𝜋 pi )‫(اپیئ‬ r radius of the cylinder ‫ل‬‫ی‬‫س‬( )‫رطق‬‫فصن‬‫اک‬‫ر‬‫ڈ‬‫ی‬ 4 𝑉 = 𝑙3 𝑉 Volume of cube )‫مجح‬‫اک‬‫(بعکم‬ 𝑙 length of each side )‫ابملیئ‬‫یک‬‫علض‬‫(رہ‬ 5 𝑉 = 𝜋𝑟2 ℎ 𝑉 Volume of cylinder ‫اک‬‫ر‬‫ڈ‬‫ی‬‫ل‬‫ی‬‫س‬( )‫مجح‬ 𝜋 pi )‫(اپیئ‬ r radius of the cylinder )‫رطق‬‫فصن‬‫اک‬‫ر‬‫ڈ‬‫ی‬‫ل‬‫ی‬‫س‬( ℎ height or length of cylinder )‫ابملیئ‬‫ای‬‫اواچنیئ‬‫یک‬‫ر‬‫ڈ‬‫ی‬‫ل‬‫ی‬‫س‬( 6 𝑉 = 1 3 𝑙2 ℎ 𝑉 Volume of pyramid )‫مجح‬‫اک‬‫(رخموط‬ 𝑙 length of each side of base )‫ابملیئ‬‫یک‬‫علض‬‫رہ‬‫ےک‬‫(اقدعہ‬ ℎ height or length of pyramid )‫ابملیئ‬‫ای‬‫اواچنیئ‬‫یک‬‫(رخموط‬ 7 𝑣 = 𝑆 𝑡 𝑣 average speed (‫راتفر‬‫)اوطس‬ 𝑆 distance (‫)افہلص‬ 𝑡 time (‫)وتق‬ 8 𝑎 = 𝑣𝑓 − 𝑣𝑖 𝑡 or 𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡 𝑣𝑓 final velocity (‫والیٹس‬‫)آرخی‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 𝑎 acceleration (‫)ارساع‬ 𝑡 time (‫)وتق‬ 9 𝑆 = 𝑣𝑖𝑡 + 1 2 𝑎𝑡2 𝑆 distance (‫)افہلص‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 𝑡 time (‫)وتق‬ 𝑎 acceleration (‫)ارساع‬
  • 3.
    GBSS NO.3 SHAHFAISAL COLONY NO.4, KARACHI 3 10 2𝑎𝑆 = 𝑣𝑓 2 − 𝑣𝑖 2 𝑎 acceleration (‫)ارساع‬ 𝑆 distance (‫)افہلص‬ 𝑣𝑓 final velocity (‫والیٹس‬‫)آرخی‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 11 𝑣𝑓 = 𝑣𝑖 + 𝑔𝑡 𝑣𝑓 final velocity (‫والیٹس‬‫)آرخی‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝑡 time (‫)وتق‬ 12 ℎ = 𝑣𝑖𝑡 + 1 2 𝑔𝑡2 ℎ height (‫)دنلبی‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 𝑡 time (‫)وتق‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 13 2𝑔ℎ = 𝑣𝑓 2 − 𝑣𝑖 2 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) ℎ height (‫)دنلبی‬ 𝑣𝑓 final velocity (‫والیٹس‬‫)آرخی‬ 𝑣𝑖 initial velocity (‫والیٹس‬‫)ادتبایئ‬ 14 𝐹 = 𝑚𝑎 𝐹 Force (‫)وقت‬ 𝑚 mass (‫)تیمک‬ 𝑎 acceleration (‫)ارساع‬ 15 𝑊 = 𝑚𝑔 𝑊 Weight (‫)وزن‬ 𝑚 mass (‫)تیمک‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 16 𝑝 = 𝑚𝑣 𝑝 Momentum (‫م‬ ‫ٹ‬‫ن‬‫ی‬‫م‬ ‫)وم‬ 𝑚 mass (‫)تیمک‬ 𝑣 speed (‫)راتفر‬ 17 𝐹 = 𝑝𝑓 − 𝑝𝑖 𝑡 𝐹 Force (‫)وقت‬ 𝑝𝑓 final momentum )‫م‬ ‫ٹ‬‫ن‬‫ی‬‫م‬ ‫وم‬‫(آرخی‬ 𝑝𝑖 Initial momentum )‫م‬ ‫ٹ‬‫ن‬‫ی‬‫م‬ ‫وم‬‫(ادتبایئ‬ 𝑡 time )‫(وتق‬
  • 4.
    GBSS NO.3 SHAHFAISAL COLONY NO.4, KARACHI 4 18 𝑚1𝑢1 + 𝑚2𝑢2 = 𝑚1𝑣1 + 𝑚2𝑣2 𝑚1 mass of the first body (‫تیمک‬‫یک‬‫مسج‬‫)ےلہپ‬ 𝑢1 speed of first body before collision (fire) ‫راتفر‬‫یک‬‫مسج‬‫ےلہپ‬،‫ےلہپ‬‫ےس‬)‫(افرئ‬‫رکٹاےن‬ 𝑚2 mass of the second body (‫تیمک‬‫یک‬‫مسج‬‫)دورسے‬ 𝑢2 speed of second body before collision (fire) ‫راتفر‬‫یک‬‫مسج‬‫دورسے‬،‫ےلہپ‬‫ےس‬)‫(افرئ‬‫رکٹاےن‬ 𝑣1 speed of first body after collision (fire) ‫راتفر‬‫یک‬‫مسج‬‫ےلہپ‬،‫دعب‬‫ےک‬)‫(افرئ‬‫رکٹاےن‬ 𝑣2 speed of second body after collision (fire) ‫راتفر‬‫یک‬‫مسج‬‫دورسے‬،‫دعب‬‫ےک‬)‫(افرئ‬‫رکٹاےن‬ 19 𝐹 𝑠 = 𝜇𝑅 𝐹 𝑠 Force of friction (‫وقت‬‫یک‬‫)رڑگ‬ 𝜇 Coefficient of friction (‫رشح‬‫یک‬‫)رڑگ‬ 𝑅 Normal reaction ( ‫ومعدی‬ ‫لمع‬ِّّ‫د‬‫ر‬ ) 20 𝑅 = 𝑊 or 𝑅 = 𝑚𝑔 𝑅 Normal reaction (‫لمع‬ِّّ‫د‬‫ر‬‫)ومعدی‬ 𝑊 Weight (‫)وزن‬ 𝑚 mass (‫)تیمک‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 21 𝑎𝑐 = 𝑣2 𝑟 𝑎𝑐 Centripetal acceleration (‫ارساع‬‫املئ‬‫)رمزک‬ 𝑣 speed (‫)راتفر‬ 𝑟 radius (‫رطق‬‫)فصن‬ 22 𝐹 𝑐 = 𝑚𝑣2 𝑟 𝐹 𝑐 Centripetal Force (‫وقت‬‫املئ‬‫)رمزک‬ 𝑚 mass (‫)تیمک‬ 𝑣 speed (‫)راتفر‬ 𝑟 radius (‫رطق‬‫)فصن‬ 23 𝐹 𝑥 = 𝐹 𝑐𝑜𝑠 𝜃 𝐹 𝑥 horizontal or x component (‫زج‬ -x) 𝐹 Force (‫)وقت‬ 𝜃 angle (‫)زاوہی‬ 24 𝐹 𝑦 = 𝐹 𝑠𝑖𝑛 𝜃 𝐹 𝑦 vertical or y component (‫زج‬ -y) 𝐹 Force (‫)وقت‬ 𝜃 angle (‫)زاوہی‬ 25 𝐹 = √𝐹 𝑥 2 + 𝐹 𝑦 2 𝐹 magnitude of 𝐹 ⃗ (‫تمیق‬‫دعدی‬‫یک‬ 𝐹 ⃗) 𝐹 𝑥 horizontal or x component (‫زج‬ -x) 𝐹 𝑦 vertical or y component (‫زج‬ -y)
  • 5.
    GBSS NO.3 SHAHFAISAL COLONY NO.4, KARACHI 5 26 𝜃 = tan−1 𝐹 𝑦 𝐹 𝑥 𝜃 direction of 𝐹 ⃗ ( ‫یک‬ ‫تمس‬ 𝐹 ⃗) 𝐹 𝑦 vertical or y component (‫زج‬ -y) 𝐹 𝑥 horizontal or x component (‫زج‬ -x) 27 𝜏 = 𝐹 × 𝑑 Or 𝜏 = 𝐹 × 𝐿 𝜏 torque (‫)اٹرک‬ 𝐹 Force (‫)وقت‬ 𝑑 or L Length of moment arm ( ‫آرم‬‫ومٹنم‬ ‫ابملیئ‬‫یک‬ ) 28 𝜏 = 𝐹 × 𝑑 𝜏 moment of couple or Torque ( ‫اک‬‫لپک‬ ‫اٹرک‬ ) 𝐹 Force (‫)وقت‬ 𝑑 length of the moment arm of the couple )‫آرم‬‫(لپک‬ 29 Clockwise moments = anticlockwise moments 𝐹1 × 𝑑1 = 𝐹2 × 𝑑2 𝐹1 1st Force or weight )‫وزن‬‫ای‬‫وقت‬‫(یلہپ‬ 𝑑1 Moment arm of 𝐹1)‫آرم‬‫ومٹنم‬‫اک‬ ‫وقت‬‫(یلہپ‬ 𝐹2 2nd Force or weight )‫وزن‬‫ای‬‫وقت‬‫(دورسی‬ 𝑑2 Moment arm of 𝐹2 )‫آرم‬‫ومٹنم‬‫اک‬‫وقت‬‫(دورسی‬ 30 First condition of equilibrium ∑ 𝐹 𝑥 = 0 , ∑ 𝐹 𝑦 = 0 ∑ 𝐹 = 0 ∑ 𝐹 𝑥 Sum of x components of Forces ( ‫ا‬ ‫زج‬ ‫ومجمہع‬‫اک‬‫ا‬ -x ‫وقوت‬ ‫ےک‬‫ں‬ ) ∑ 𝐹 𝑦 Sum of y components of Forces )‫ومجمہع‬‫اک‬‫ازجا‬ -y ‫وقوت‬ ‫ں‬ ‫ےک‬ ) ∑ 𝐹 Sum of all Forces )‫ومجمہع‬‫اک‬‫وقوتں‬‫(امتم‬ 31 Second condition of equilibrium ∑ 𝜏 = 0 ∑ 𝜏 Sum of all torques (‫ومجمہع‬‫اک‬‫اٹروکں‬‫)امتم‬ 32 𝑃 = 𝐹 𝐴 𝑃 Pressure )‫(دابؤ‬ 𝐹 Force )‫(وقت‬ 𝐴 Area )‫(رہبق‬ 33 𝑃 = 𝑑𝜌𝑔 𝑃 Pressure )‫(دابؤ‬ 𝑑 depth )‫(رہگایئ‬ 𝜌 Density )‫(اثکتف‬ 𝑔 Acceleration due to gravity )‫ارساع‬‫ی‬‫قل‬‫ث‬( 34 𝐹 = 𝐾𝑥 𝐹 Force (‫)وقت‬ 𝐾 spring constant (‫لقتسم‬‫اک‬‫)ارپسگن‬ 𝑥 Extension (‫اچنھکؤ‬‫ای‬‫)ڑباھؤ‬
  • 6.
    GBSS NO.3 SHAHFAISAL COLONY NO.4, KARACHI 6 35 𝐹 = 𝐺 𝑚1𝑚2 𝑟2 𝐹 Force of gravitation (‫وقت‬‫)اجتذیب‬ 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝑚1 mass of the first body (‫تیمک‬‫یک‬‫مسج‬‫)ےلہپ‬ 𝑚2 mass of the second body (‫تیمک‬‫یک‬‫مسج‬‫)دورسے‬ 𝑟 distance (‫)افہلص‬ 36 𝑀𝑒 = 𝑔𝑅𝑒 2 𝐺 𝑀𝑒 Mass of earth (‫تیمک‬‫یک‬‫)زنیم‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝑅𝑒 Radius of earth (‫رطق‬‫فصن‬‫اک‬‫)زنیم‬ 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 37 𝑀𝑝 = 𝑔𝑅𝑝 2 𝐺 𝑀𝑝 Mass of planet ( ‫ارے‬ ّ‫س‬ ‫تیمک‬‫یک‬ ) 𝑔 acceleration due to gravity on planet (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝑅𝑝 Radius of planet ( ‫ارے‬ ّ‫س‬ ‫رطق‬‫فصن‬‫اک‬ ) 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 38 𝑔𝑒 = 𝐺𝑀𝑒 𝑅𝑒 2 𝑔𝑒 acceleration due to gravity on earth (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝑀𝑒 Mass of earth (‫تیمک‬‫یک‬‫)زنیم‬ 𝑅𝑒 Radius of earth (‫رطق‬‫فصن‬‫اک‬‫)زنیم‬ 39 𝑔𝑝 = 𝐺𝑀𝑝 𝑅𝑝 2 𝑔𝑝 acceleration due to gravity on planet (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝑀𝑝 Mass of planet ( ‫ارے‬ ّ‫س‬ ‫تیمک‬‫یک‬ ) 𝑅𝑝 Radius of planet ( ‫ارے‬ ّ‫س‬ ‫رطق‬‫فصن‬‫اک‬ ) 40 𝑣 = √ 𝐺𝑀 𝑅 + ℎ 𝑣 Speed of satellite ‫(ونصمیع‬ )‫راتفر‬‫یک‬‫ارے‬ ّ‫س‬ 𝐺 Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝑀 Mass of planet(earth) ( ‫ارے‬ ّ‫س‬ ‫تیمک‬‫یک‬ ) 𝑅 Radius of planet(earth) ( ‫ارے‬ ّ‫س‬ ‫رطق‬‫فصن‬‫اک‬ ) ℎ height(altitude) of satellite )‫(دنلبی‬ 41 𝑣𝑐 = √𝑔𝑅 𝑣𝑐 Critical velocity of satellite ‫(ونصمیع‬ )‫والیٹس‬‫افلص‬‫یک‬‫ارے‬ ّ‫س‬ 𝑔 Acceleration due to gravity )‫ارساع‬‫ی‬‫قل‬‫ث‬( 𝑅 Radius of planet(earth) ( ‫ارے‬ ّ‫س‬ ‫رطق‬‫فصن‬‫اک‬ ) 42 𝑃1𝑉1 = 𝑃2𝑉2 𝑃1 Initial Pressure (‫دابؤ‬‫)ادتبایئ‬ 𝑉1 Initial Volume (‫مجح‬‫)ادتبایئ‬ 𝑃2 Final Pressure (‫دابؤ‬‫)آرخی‬ 𝑉2 Final Volume (‫مجح‬‫)آرخی‬
  • 7.
    GBSS NO.3 SHAHFAISAL COLONY NO.4, KARACHI 7 43 𝑊 = 𝐹. 𝑑 or 𝑊 = 𝐹𝑑 𝑐𝑜𝑠 𝑐𝑜𝑠 𝜃 𝑊 Work done (‫)اکم‬ 𝐹 Force (‫)وقت‬ 𝑑 Displacement (‫)اٹہؤ‬ 𝜃 angle (‫)زاوہی‬ 44 𝑃 = 𝑊 𝑡 𝑃 Power (‫)اطتق‬ 𝑊 Work done (‫)اکم‬ 𝑡 time (‫)وتق‬ 45 𝐾. 𝐸 = 1 2 𝑚𝑣2 𝐾. 𝐸 Kinetic Energy (‫وتاانیئ‬‫)رحیک‬ 𝑚 mass (‫)تیمک‬ 𝑣 velocity (‫)والیٹس‬ 46 𝑃. 𝐸 = 𝑚𝑔ℎ 𝑃. 𝐸 Potential Energy (‫وتاانیئ‬‫ل‬‫ش‬‫ن‬‫ی‬‫ٹ‬ ‫وپ‬‫ای‬‫)یفخم‬ 𝑚 mass (‫)تیمک‬ 𝑔 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) ℎ height (‫)دنلبی‬ 47 Ƞ = 𝐸2 𝐸1 × 100 Ƞ Efficiency )‫(اکررکدیگ‬ 𝐸2 Energy as output )‫وتاانیئ‬‫ٹپ‬‫(آؤٹ‬ 𝐸1 Energy as input )‫وتاانیئ‬‫ٹپ‬‫(ان‬ 48 ℉ = 1.8℃ + 32 ℉ Temperature in Fahrenheit ( ‫رحات‬ٔ‫ہج‬‫در‬ ‫اہٹیئ‬‫افرن‬ ‫ںیم‬ ) ℃ Temperature in Celsius ( ‫ی‬‫س‬ ‫رحات‬ٔ‫ہج‬‫در‬ ‫س‬‫شن‬‫ل‬ ‫ںیم‬ ) 49 𝐾 = ℃ + 273 𝐾 Temperature in Kelvin (‫ںیم‬‫ولیکن‬‫رحارت‬ٔ‫ہج‬‫)در‬ ℃ Temperature in Celsius ( ‫ی‬‫س‬ ‫رحات‬ٔ‫ہج‬‫در‬ ‫س‬‫شن‬‫ل‬ ‫ںیم‬ ) 50 ∆𝐿 = 𝛼L∆𝑇 ∆𝐿 change or increase in Length ( ‫ںیم‬‫ابملیئ‬ ‫ای‬‫دبتیلی‬ ‫ااضہف‬ ) 𝛼 Coefficient of linear expansion (‫رشح‬‫یک‬‫الیھپؤ‬‫)وطیل‬ L Initial or original Length (‫ابملیئ‬‫)ادتبایئ‬ ∆𝑇 change in Temperature ( ‫رحارت‬‫درہج‬ ‫ںیم‬ ‫ای‬‫دبتیلی‬ ‫ااضہف‬ ) 51 ∆𝑉 = 𝛽𝑉∆𝑇 ∆𝑉 change or increase in Volume ( ‫مجح‬ ‫ںیم‬ ‫ای‬‫دبتیلی‬ ‫ااضہف‬ ) 𝛽 Coefficient of volumetric expansion ( ‫ی‬‫م‬‫ج‬‫ح‬ ‫رشح‬‫یک‬‫الیھپؤ‬ ) 𝑉 Initial or original Volume ( ‫ادتبایئ‬ ‫مجح‬ ) ∆𝑇 change in Temperature ( ‫رحارت‬‫درہج‬ ‫ںیم‬ ‫ای‬‫دبتیلی‬ ‫ااضہف‬ ) 52 𝛽 = 3𝛼 𝛽 Coefficient of volumetric expansion (‫رشح‬‫یک‬‫الیھپؤ‬‫ی‬‫م‬‫ج‬‫ح‬ ) 𝛼 Coefficient of linear expansion (‫رشح‬‫یک‬‫الیھپؤ‬‫)وطیل‬
  • 8.
    GBSS NO.3 SHAHFAISAL COLONY NO.4, KARACHI 8 53 𝑐 = ∆𝑄 𝑚∆𝑇 𝑐 Specific heat capacity )‫وصخمہص‬ ِّ ‫(رحارت‬ ∆𝑄 Amount of heat )‫دقمار‬‫یک‬‫(رحارت‬ 𝑚 mass )‫(تیمک‬ ∆𝑇 Change in Temperature )‫دبتیلی‬‫ںیم‬‫رحارت‬‫(درہج‬ Some important values for numericals Quantity Symbol Value Acceleration due to gravity )‫ارساع‬‫ی‬‫قل‬‫ث‬( 𝑔 10 ms-2 (approximately) Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝐺 6.673 x 10-11 Nm2kg-2 Radius of earth (‫رطق‬‫فصن‬‫اک‬‫)زنیم‬ 𝑅𝑒 6.38 x 106 m Mass of earth (‫تیمک‬‫یک‬‫)زنیم‬ 𝑀𝑒 6.0 x 1024 kg Specific heat capacity of water )‫وصخمہص‬ ِّ ‫رحارت‬‫یک‬‫(اپین‬ 𝑐 4200 Jkg-1 oc-1 Specific heat capacity of copper )‫وصخمہص‬ ِّ ‫رحارت‬‫یک‬‫(اتہبن‬ 𝑐 385 Jkg-1 oc-1
  • 9.
    GBSS NO.3 SHAHFAISAL COLONY NO.4, KARACHI 9 Some Units of Physical Quantities For Numericals Quantity Quantity Symbol Unit Unit Symbol Length )‫(ابملیئ‬ L meter ‫(رٹیم‬ ) m Temperature )‫رحارت‬‫(درہج‬ T Kelvin )‫(ولیکن‬ K Electric current )‫رکٹن‬‫(ربیق‬ I Ampere )‫ر‬‫ی‬‫ی‬‫من‬‫ی‬ ‫(ا‬ A mass )‫(تیمک‬ 𝑚 kilogram )‫(ولکرگام‬ kg time (‫)وتق‬ 𝑡 second )‫(ڈنکیس‬ s amount of substance )‫دقمار‬‫یک‬‫(ےش‬ n mole )‫(ومل‬ mol Luminous intensity ‫دش‬‫یک‬‫(روینش‬ )‫ت‬ 𝐼𝑣 candela )‫(ڈنیکالی‬ cd Volume ( )‫مجح‬ 𝑉 cubic meter )‫رٹیم‬‫(بعکم‬ m3 Energy )‫(وتاانیئ‬ 𝐸 Joule )‫(وجل‬ J radius ( )‫رطق‬‫فصن‬ r meter ‫(رٹیم‬ ) m density )‫(اثکتف‬ 𝜌 kilogram per cubic meter )‫رٹیم‬‫بعکم‬‫یف‬‫(ولکرگام‬ kg/m3 speed (‫)راتفر‬ 𝑣 meter per second )‫ڈنکیس‬‫یف‬‫(رٹیم‬ ms-1 distance (‫)افہلص‬ 𝑆 or d meter ‫(رٹیم‬ ) m Area ( )‫رہبق‬ 𝐴 meter square )‫رٹیم‬‫(رمعب‬ m2 acceleration (‫)ارساع‬ 𝑎 meter per second square )‫ڈنکیس‬‫رمعب‬‫یف‬‫(رٹیم‬ ms-2 acceleration due to gravity (‫ارساع‬‫ی‬‫قل‬‫ث‬) 𝑔 meter per second square )‫ڈنکیس‬‫رمعب‬‫یف‬‫(رٹیم‬ ms-2 height (‫)دنلبی‬ ℎ meter ‫(رٹیم‬ ) m Force (‫)وقت‬ 𝐹 Newton )‫(ویننٹ‬ N Weight (‫)وزن‬ 𝑊 Newton )‫(ویننٹ‬ N Momentum (‫م‬ ‫ٹ‬‫ن‬‫ی‬‫م‬ ‫)وم‬ 𝑝 kilogram meter per second )‫ڈنکیس‬‫یف‬‫رٹیم‬‫(ولکرگام‬ kgm/s Normal reaction (‫لمع‬ِّّ‫د‬‫ر‬‫)ومعدی‬ 𝑅 Newton )‫(ویننٹ‬ N torque (‫)اٹرک‬ 𝜏 Newton meter )‫رٹیم‬‫(ویننٹ‬ Nm Pressure )‫(دابؤ‬ 𝑃 Pascal )‫(اپلکس‬ Pa depth )‫(رہگایئ‬ 𝑑 meter ‫(رٹیم‬ ) m Extension (‫اچنھکؤ‬‫ای‬‫)ڑباھؤ‬ 𝑥 meter ‫(رٹیم‬ ) m Gravitational constant (‫لقتسم‬‫)اجتذیب‬ 𝐺 Newton meter square per kilogram square )‫ولکرگام‬‫رمعب‬‫یف‬‫رٹیم‬‫رمعب‬‫(ویننٹ‬ Nm2kg-2 Work done (‫)اکم‬ 𝑊 Joule )‫(وجل‬ J displacement (‫)اٹہؤ‬ 𝑑 meter ‫(رٹیم‬ ) m
  • 10.
    GBSS NO.3 SHAHFAISAL COLONY NO.4, KARACHI 10 Power (‫)اطتق‬ 𝑃 watt )‫(واٹ‬ w Kinetic Energy (‫وتاانیئ‬‫)رحیک‬ 𝐾. 𝐸 Joule )‫(وجل‬ J velocity (‫)والیٹس‬ 𝑣 meter per second )‫ڈنکیس‬‫یف‬‫(رٹیم‬ ms-1 Potential Energy (‫وتاانیئ‬‫ل‬‫ش‬‫ن‬‫ی‬‫ٹ‬ ‫وپ‬‫ای‬‫)یفخم‬ 𝑃. 𝐸 Joule )‫(وجل‬ J Coefficient of linear expansion (‫رشح‬‫یک‬‫الیھپؤ‬‫)وطیل‬ 𝛼 per degree Celsius )‫س‬‫شن‬‫ل‬‫ی‬‫س‬ ‫ڈرگی‬‫(یف‬ oc-1 Coefficient of volumetric expansion ( ‫ی‬‫م‬‫ج‬‫ح‬ ‫رشح‬‫یک‬‫الیھپؤ‬ ) 𝛽 per degree Celsius )‫س‬‫شن‬‫ل‬‫ی‬‫س‬ ‫ڈرگی‬‫(یف‬ oc-1 Specific heat capacity )‫وصخمہص‬ ِّ ‫(رحارت‬ 𝑐 Joule per kilogram per degree Celsius )‫س‬‫شن‬‫ل‬‫ی‬‫س‬ ‫ڈرگی‬‫یف‬‫ولکرگام‬‫یف‬‫(وجل‬ J/kgoc-1 Amount of heat )‫دقمار‬‫یک‬‫(رحارت‬ ∆𝑄 Joule )‫(وجل‬ J