Key Assumptions ] The Hydroplate Theory: Granite, the primary continental rock, has a grayish-to-pinkish color.
JEE Mathematics Syllabus Algebra Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.
Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.
Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.
Logarithms and their properties. Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients. Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables.
Addition and multiplication rules of probability, conditional probability, independence of events, computation of probability of events using permutations and combinations. Trigonometry Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations.
Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions principal value only. Analytical geometry Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin.
Equation of a straight line in various forms, angle between two lines, distance of a point from a line. Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines, centroid, orthocentre, incentre and circumcentre of a triangle.
Equation of a circle in various forms, equations of tangent, normal and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.
Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal. Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.
Differential calculus Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions.
Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, l'Hospital rule of evaluation of limits of functions.
Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property of continuous functions. Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions.
Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, applications of Rolle's Theorem and Lagrange's Mean Value Theorem.
Integral calculus Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, application of the Fundamental Theorem of Integral Calculus. Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas involving simple curves.
Formation of ordinary differential equations, solution of homogeneous differential equations, variables separable method, linear first order differential equations.
Vectors Addition of vectors, scalar multiplication, scalar products, dot and cross products, scalar triple products and their geometrical interpretations.
The concept of atoms and molecules; Dalton's atomic theory; Mole concept; Chemical formulae; Balanced chemical equations; Calculations based on mole concept involving common oxidation-reduction, neutralisation, and displacement reactions; Concentration in terms of mole fraction, molarity, molality and normality.Here is a history of older questions and answers processed by "Ask the Physicist!".
If you like my answer, please consider making a donation to help support this service. The angular momentum principle says that the net torque (about the center) is equal to the moment of inertia times the angular acceleration of the disk (about the center).
With the recent publication of PHYSICS IS there are now three Ask the Physicist books! Click on the book images below for information on the content of the books and for information on ordering. The model presented in this video is designed to compare different options for the relation between banks and the public sector and different types of subsidies regarding their effects on social welfare.
Of the various modes of oscillation, our main interest is the first antisymmetric mode. This is because of two reasons: the first antisymmetric mode involves the largest amount of liquid mass movement, and as we will see in the following section, its frequency corresponds .
15e Moment of Inertia - 1 - ANGULAR ACCELERATION AND MOMENT OF INERTIA Introduction Rotating an object requires that one overcomes that object’s rotational inertia, better The tangential force Ft on the disk is the tension T of the string. By studying Figure 1.