12mve2=GMmR⟹ve=2GMR=2gRone-half m v sub e squared equals the fraction with numerator cap G cap M m and denominator cap R end-fraction ⟹ v sub e equals the square root of the fraction with numerator 2 cap G cap M and denominator cap R end-fraction end-root equals the square root of 2 g cap R end-root 6. Mechanical Properties of Solids and Fluids Ascent Formula (Capillary Rise)
P1+12ρv12+ρgh1=P2+12ρv22+ρgh2space cap P sub 1 plus one-half rho v sub 1 squared plus rho g h sub 1 equals cap P sub 2 plus one-half rho v sub 2 squared plus rho g h sub 2
vmax=rg(μs+tanθ1−μstanθ)v sub m a x end-sub equals the square root of r g of open paren the fraction with numerator mu sub s plus tangent theta and denominator 1 minus mu sub s tangent theta end-fraction close paren end-root 3. Work, Energy, and Power Work-Energy Theorem
Deriving the minimum velocity needed to leave a planet's gravitational pull.
Class 11 Physics forms the bedrock of both board exams and competitive entrance tests like JEE and NEET. While understanding concepts is crucial, mastering derivations is the secret to scoring full marks. Derivations explain the "why" and "how" behind formulas, transforming rote memorisation into logical understanding. all important derivations of physics class 11 pdf download
The speed required for a satellite to remain in orbit. Unit 6: Properties of Bulk Matter
mole of an ideal gas be heated at constant volume. The heat supplied is .By the First Law of Thermodynamics:
This section links microscopic molecular motion to macroscopic thermal properties like temperature and pressure. 1. Pressure of an Ideal Gas molecules, each of mass , inside a cube of side .A single molecule moving with velocity collides with a wall. Its change in momentum is:
): The maximum vertical distance reached. At peak height, vertical velocity Class 11 Physics forms the bedrock of both
Fundamental theorems for moments of inertia. Acceleration due to Gravity ( ): Derive the variation of with height and depth. Escape Velocity: Derive 4. Thermodynamics Work Done in an Isothermal Process: Derive Meyer's Formula: Prove 5. Oscillations & Waves Time Period of Simple Pendulum: Derive
P+12ρv2+ρgh=Constantcap P plus one-half rho v squared plus rho g h equals Constant
v=dsdt⟹ds=vdtv equals d s over d t end-fraction ⟹ d s equals v space d t : Substitute ds=(u+at)dtd s equals open paren u plus a t close paren d t Integration : Integrate from displacement , and time
s=u∫0tdt+a∫0ttdts equals u integral from 0 to t of d t plus a integral from 0 to t of t space d t : s=ut+12at2s equals u t plus one-half a t squared Third Equation: Definition : Chain rule acceleration. The speed required for a satellite to remain in orbit
v=dxdt=ddt[Asin(ωt+ϕ)]=Aωcos(ωt+ϕ)v equals d x over d t end-fraction equals d over d t end-fraction open bracket cap A sine open paren omega t plus phi close paren close bracket equals cap A omega cosine open paren omega t plus phi close paren
W=∫uv(mvdvds)ds=m∫uvv⋅dv=m[v22]uv=12mv2−12mu2=Kf−Kicap W equals integral from u to v of open paren m v d v over d s end-fraction close paren d s equals m integral from u to v of v center dot d v equals m open bracket the fraction with numerator v squared and denominator 2 end-fraction close bracket sub u to the v-th power equals one-half m v squared minus one-half m u squared equals cap K sub f minus cap K sub i 2. Potential Energy of a Spring
1. Velocity and Acceleration in Simple Harmonic Motion (SHM) Displacement equation of an oscillator:
✅ All Important Derivations of Physics Class 11 PDF Download
The work-energy theorem states that work done by a net force equals the change in kinetic energy ( Let a variable force act along the direction of motion: dW=F⋅dxspace d cap W equals cap F center dot d x By Newton's second law,