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Class 11 Physics forms the bedrock of engineering, medical, and academic competitive exams like JEE, NEET, and boards. Derivations are not just mathematical exercises; they explain why formulas work. This guide compiles the most high-yield derivations required for your exams. Unit 1: Kinematics
ma=−(mgl)x⟹a=−(gl)xm a equals negative open paren m g over l end-fraction close paren x ⟹ a equals negative open paren g over l end-fraction close paren x
12mve2=GMmR⟹ve=2GMRone-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 , we can substitute ve=2gRv sub e equals the square root of 2 g cap R end-root Unit 6: Mechanics of Solids and Fluids Bernoulli's Principle
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ω=dθdt⟹dθ=ω⋅dtomega equals the fraction with numerator d theta and denominator d t end-fraction ⟹ d theta equals omega center dot d t Substitute the first rotational equation:
v1=(m1−m2m1+m2)u1+(2m2m1+m2)u2space v sub 1 equals open paren the fraction with numerator m sub 1 minus m sub 2 and denominator m sub 1 plus m sub 2 end-fraction close paren u sub 1 plus open paren the fraction with numerator 2 m sub 2 and denominator m sub 1 plus m sub 2 end-fraction close paren u sub 2
This matches the standard Simple Harmonic Motion (SHM) acceleration equation . Comparing coefficients: Class 11 Physics forms the bedrock of engineering,
g=GR2(43πR3ρ)=43πGRρg equals the fraction with numerator cap G and denominator cap R squared end-fraction open paren four-thirds pi cap R cubed rho close paren equals four-thirds pi cap G cap R rho At a depth below the surface, the effective radius becomes . Only the inner sphere of radius exerts a net gravitational pull at this point:
R=ux⋅T=(ucosθ)⋅(2usinθg)space cap R equals u sub x center dot cap T equals open paren u cosine theta close paren center dot open paren the fraction with numerator 2 u sine theta and denominator g end-fraction close paren
gdg=R−dRspace the fraction with numerator g sub d and denominator g end-fraction equals the fraction with numerator cap R minus d and denominator cap R end-fraction Can’t copy the link right now
Mastering Class 11 Physics: Essential Derivations for Exam Success
Deriving the final velocities of two colliding bodies ( 4. System of Particles and Rotational Motion
