CBSE Class 11 Physics Mathematical Tools Notes Set B

MATHEMATICAL TOOLS

Physical constants:-

1. Mass of an electron (M_e) = 9.1x10^-31kg.

2. Mass of a proton ( M_p) = 1.6725 x 10^-27kg.

3. Mass of a neutron (M_n) = 1.6746 x 10^-27kg.

4. Charge of an electron (e) = -1.6 x 10^-19c

5. Speed of light in vacuum (c) = 3 x10⁸ m/sec.

6. Planck Constant (h) = 6.6256 x 10^-34 J x sec .

7. Universal Gravitation constant (G) = 6.67 x 10^-11 Nm²/ kg².

8. Avogadro Number (NA) = 6.023 x10²³ mol^-1.

9. Boltzmann constant (K) = 1.38 x 10^-23 J/K

10.Stefan Constant (σ) = 5.67 x 10-8 W m-2 K-4.

11. Wien Displacement Constant (b) = 2.898 x10^-3 m K

12. Solar Constant (S) = 1.388 x 103 W m^-2

13. Mass of the sun (MS) = 2x 10³⁰kg.

14. Mass of the earth (ME) = 5.98x 10²⁴kg

15. Radius of the earth (Re) = 6400 Km. = 6.4x10⁶m.

16. Density of earth 5.522x10³kg/m³.

17. Average angular velocity of the earth = 7.29x 10^-5rad./sec

18. Average distance between the sun and earth = 1.5x10¹¹m.

19. Average distance between moon and the earth =3.84x 10⁸m.

20. Magnetic Moment of the earth = 6.4x 10²¹ Amp. X m².

Conversion Coefficients

1. 1Light year = 9.46x10¹⁵m.

2. 1 A.U. = 1.496 x 10¹¹m.

3. 1Å = 10^-10m.

4. 1 Pound = 0.4536kg = 453.6 gm

5. 1 Fermi = 10^-15m.

6. 1 C.S.L.= 1.4 x Mass of the sun.

7. 1 Shake = 10^-8sec.

8. 1ev = 1.6 x10^-19 Joule.

9. 1 Horse Power = 746 Watt.

Quadratic Equation

An equation of second degree is called a quadratic equation. It is of the form

:- ax² + bx + c =0

The roots of a quadratic equation are

X = -b ±(b² + 4ac)^1/2 / 2a

Binomial Theorem

If n is any integer, positive or negative or a fraction and x is any real number, then

( 1+x)ⁿ = 1 + nx + n(n-1)x² + .. . / Ị2

If IxI <<1 , then (1+x)ⁿ = 1+ nx.

Mensuration :-

1. Area of a circle = πr² =π D²/4

2. Surface area of a sphere = 4πr² = πD²

3. Volume of a sphere = 4/3 πr³

4. Surface area of a cylinder = 2πr(r+l)

5. Volume of a cylinder =π r² l

6. Curved surface area of a cone = πrl

7. Volume of a cone = 1/3πr²h

8. Surface area of a cube = 6x(side)²

9. Volume of a cube = (side)³

Fundamental Trigonometric relations

Fundamental Trigonometric relations

MATHEMATICAL TOOLS

MATHEMATICAL TOOLS 2

MATHEMATICAL TOOLS 4

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