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^Rest & motion

^Rest & motion

If position of body changes w.r.t. surroundings with the time then it is said to be moving otherwise at rest. Rest & motion are relative. A person sitting in a moving vehicle is at rest w.r.t. other persons in sitting same vehicle while is in motion w.r.t. other persons standing on road. If the position of a body doesn’t change with respect to all objects in the universe, then it is said to be in absolute rest. Absolute rest is impossible. If the position of a body doesn’t change with respect to one or more things in the universe, then it is said to be in relative rest. Relative rest is possible.

^Parallel combination of resistors

Parallel combination of resistors

The voltage is same across each circuit element is same but current is different & is inversely proportional to resistance of that part.

V = V1 = V2 = V3 = I1R1 = I2R2 = I3R3

&

Fact the maximum number of combination one can have, using all n – resistors at a time is:

(a)  2 (n – 1)      [For n – identical resistors

(b) 2n                    For n – different resistors

^Astronomical Unit (AU)

^Astronomical Unit (AU)

It is the mean distance of the Earth from the Sun.

1 AU = 1.496 x 1011 m » 1.5 x 1011 m

 

^Limitations of dimensions

^Limitations of dimensions

  • Dimensional analysis does not give any information about the scalar or vector nature of the quantity.
  • Dimensions for    v = u + at etc. can’t be calculated in exact form.
  • Dimensional formulae of the quantities depending on more than three variables cannot be obtained.
  • Dimensional formulae of the quantities involving trigonometric logarithmic or exponential functions cannot be calculated.
  • Value of proportionality constant can’t be calculated.

It doesn’t distinguish between the physical quantities having same dimensions.

*Dimensional Constants

*Dimensional Constants

All constants are not dimensionless. The physical quantities which have constant values and dimensions as well are called dimensional constants.

e.g. Planck’s constant, Boltzmann’s constant & Gravitational constant etc.

*One steradian

*One steradian

One steradian (sr)is the solid angle subtended at the centre of a sphere by that surface of the sphere which is equal in area to square of the radius of the sphere.

         

^Standard integrals

^Standard integrals

 

*Inverse function

*Inverse function

Function of the form,

have the shown variation. All the curves pass through the point (1, 1). For n > 1 the graph lies above the rectangular hyperbola

(n =1) in the region

0 < x < 1 and then lies below it in the region x > 1. For 0 < n < 1 the graph first lies below the hyperbola in the region 0 < x < 1 and then lies above the hyperbola in the region x > 1.

*Vertical line

*Vertical line

Function x = a represents a vertical line located right side of y axis if a = +ve & left side of y axis if a = – ve.

*Arithmetic progression

*Arithmetic progression

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