g′g=GM(R+h)2GMR2=R2(R+h)2=R2R2(1+hR)2=(1+hR)-2the fraction with numerator g prime and denominator g end-fraction equals the fraction with numerator the fraction with numerator cap G cap M and denominator open paren cap R plus h close paren squared end-fraction and denominator the fraction with numerator cap G cap M and denominator cap R squared end-fraction end-fraction equals the fraction with numerator cap R squared and denominator open paren cap R plus h close paren squared end-fraction equals the fraction with numerator cap R squared and denominator cap R squared open paren 1 plus the fraction with numerator h and denominator cap R end-fraction close paren squared end-fraction equals open paren 1 plus the fraction with numerator h and denominator cap R end-fraction close paren to the negative 2 power Using the Binomial Theorem for (ignoring higher-order terms):
vy2=uy2−2gH⟹0=(usinθ)2−2gHv sub y squared equals u sub y squared minus 2 g cap H ⟹ 0 equals open paren u sine theta close paren squared minus 2 g cap H
12gT2=usinθTone-half g cap T squared equals u sine theta cap T
∫uvdv=a∫0tdtintegral from u to v of d v equals a integral from 0 to t of d t all important derivations of physics class 11 pdf download
To prevent vehicles from skidding on sharp curves, roads are tilted inward at an angle Consider a car of mass on a road banked at angle with a friction coefficient .Resolving the Normal force ( ) and Frictional force ( ) vertically and horizontally: Vertical equilibrium: Horizontal centripetal force:
Consider a rigid body rotating about a fixed axis. For a single constituent particle of mass at distance
g′g=43πG(R−d)ρ43πGRρ=R−dRthe fraction with numerator g prime and denominator g end-fraction equals the fraction with numerator four-thirds pi cap G open paren cap R minus d close paren rho and denominator four-thirds pi cap G cap R rho end-fraction equals the fraction with numerator cap R minus d and denominator cap R end-fraction Solve 5 derivations daily, and by the end
The restoring force of an ideal spring follows Hooke’s Law:
For a streamlined flow of an ideal fluid, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant.
dW=−Fs⋅dx=−(−kx)dx=kx⋅dxd cap W equals negative cap F sub s center dot d x equals negative open paren negative k x close paren d x equals k x center dot d x Solve 5 derivations daily
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:
Download a reliable PDF today, print the 44 derivations listed above, and stick it on your wall. Solve 5 derivations daily, and by the end of 9 days, you will guarantee 25+ out of 35 marks in your numerical/theory paper.
) is the rotational equivalent of linear force.Position vector .By definition: