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Sunday, February 24, 2013

Plus1 previous Question papers

Wednesday, July 4, 2012

Plus 1 : UNITS AND MEASUREMENTS


CHAPTER 1 :UNITS AND MEASUREMENTS



  1. WHAT IS A PHYSICAL QUANTITY?  GIVE EXAMPLES?

Any thing that can be measured is a physical quantity.  Example : length, mass, time
Velocity, density

  1. What is a Unit?  Give examples?

Units are certain reference standards used for making measurements.
Example:  m/s, kg/ m3,  Km, Kg


  1. What are fundamental quantities and fundamental Units?
   The physical quantities mass, length and time are known as fundamental quantities.
They are called so because, Units of all other quantities in mechanics can be derived from fundamental units.  Also they can not be sub divided in to smaller units

Units of fundamental quantities are known as fundamental units.
 (meter , kilogram, second )

  1. What are derived quantities and derived units?

      Physical quantities that can be expressed in terms of fundamental quantities are
     known as derived quantities.
      (example : m/s  , m/s2, m3 )

      Note:   Two parts for measured result:
     Any measurement has two parts
  1. Its magnitude
  2. Its Unit

If we decrease the size of the unit, the numerical; value will increase.

1 Km  = 1000 m

Here Km is a large unit of length, while magnitude is 1
But, meter is a small unit of length and its magnitude is 1000

Smaller the size of the unit, greater is its numerical value.

  1. What are the characteristics of a unit , that is chosen for making measurement ?

The unit that is chosen for making a measurement should have the following properties:

    1. It must be well defined.
    2. It should be of suitable size
    3. It should be accepted internationally
    4. It should not change with change in temperature, pressure ,etc


  1. What are the different system of units ?
CGS – Centimeter, gram , second
       FPS – Foot, Pound, Second
       MKS – Meter, Kilogram, second

  1. What are the physical quantities and units in SI system?


7 Basis physical quantities  of SI unit system are

Length
meter
M
Mass
Kilogram
Kg
Time
Second
S
Temperature
Kelvin
K
Electric current
Ampere
A
Luminous intensity
Candela
Cd
Quantity of matter
Mole
mol

2 Supplementary quantities of SI system are

Plane angle
Radian
rad
Solid angle
Steradians
sr



  1. Define 1 meter in 3 ways ?

1)      It is 1 / (107) th of the distance from north pole to equator of earth

1 meter - old definition



2)      1 meter is the distance between two lines marked on a Platinum-Iridium rod
Kept at a constant temperature of 273.16 K and at  1 bar pressure in the
International bureau of weights and measures at severs near Paris in France.
3)      1 meter is  equal to 1650763.73 times the wavelength of orange red light
Emitted by Kr-86 source, kept at triple point of Nitrogen.

 
Many units to measure length

1 Km = 103 m
1 deci meter = 10-1 m
1 centi meter = 10-2 m
1 milli meter = 10-3 m
1 micro meter = 10-6 m
1 angstrom = 10-10 m
1 fermi = 10-15 m


9 .   Define 1 Kg


1 Kg is equal to the mass of Platinum – Iridium cylinder of diameter equal to its height, kept at international bureau of weights and measures.


Definition of 1 Kg

Many units to measure mass

1 Kg = 1000 gm
1 Ton = 1000 Kg
1 Quintal = 100 Kg
1 gm = 1000 mg

       10. Define 1 second

(a)    1 second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of  Cesium – 133 atom in ground state.
(b)   1 second is defined as 1 / (86,400) th  part of a mean solar day.

Mean solar day is the average of all solar days in a single year.
    
11. Define  1 Ampere

1 Ampere is that constant current which if maintained in two straight parallel conductors of infinite length , of negligible cross section and placed 1 m apart in vacuum , would produce between these conductors a force equal to  2 x 10 -7 N




12. Define 1 Radian

1 Radian is the plane angle between two radii of a circle which cutts off on the circumference an arc equal to the radius of the circle.

1 radian

360 degree  =  2 ∏  radian
There for,  1 radian  = 180 / ∏  degree

13. Define 1 Steradian

1 Steradian is the solid angle which with its vertex at the center of a sphere cuts off an area on the surface of the sphere equal to that of a square having sides of length equal to the radius of the sphere.

Order of Magnitude

To estimate how big or small a given physical quantity , we can use the idea of
Order of magnitude.

The given magnitude is expressed as    a x 10 b

Where  ‘a’ is a number between 1 and 10

Number  ‘b’ can be +ve or –ve

If  a >  5 , then order of magnitude = b+1
If  a < =5, then order of magnitude = b

For example :

    Diameter of earth 1.28 x 107 m
     Order of magnitude = 7 and it is of the Order of 107
 
     Distance between two points is measured as  7.25 x 10-10 m
      Its order of magnitude is 10-9  and It is of the Order of 10-9

Sunday, July 31, 2011

Entrance Question Answers: Motion in Stright line

Q1.
Water drops from the roof of a building 10 m high. The drops fall at regular intervals of time, the first drop striking the floor at the instant the 4th drop begins to fall. Find positions of individual drops,when a drop strikes the floor?


Let t is the time interval between A,B,C and D positions
That means, 3t second taken to travel from A to D.
That is, 10 m traveled in 3t seconds.

S = ut + 1/2 a t^2 

10 = 0 + 1/2 x 10 (3t)^2

10 = 5 x 9 x t^2

t^2 = 2/9




 Now,  

S1 = ut + 1/2 g t^2 

S1 = 0 + 1/2 x 10 x  2/9 = 10/9 m (AB length)

 S1 +S2 = 0+1/2x10x(2t)^2
 S1 +S2 = 0+1/2x10x(2x2/9)^2 = 40/9 m (AC length)

S1+S2+S3 = 0+1/2x10x(3t)^2
S1+S2+S3 = 0+1/2x10x(32/9)^2 = 10m  (AD length)
 


Tuesday, June 14, 2011

Electric charge density

Suman m.s said...

sir...one doubt in problem follows

The earth has on electric charge that causes an electric field near its surface of the order of 100 vm-1.What is the surface density of charge on earth of earth is a conducting sphere? pls help me 2 solve it

Anish V Rajan said...

Take earth as a conducting sphere of surface charge density (sigma)

Assume total charge that is spread on the surface is Now concentrated on the center. Find Electric field at the surface by usual equation


Sunday, March 20, 2011

Work Power and Energy

Q1 Certain physical quantities are listed below. Select any three pairs of physical quantity with same dimension.
(1) Stress (2) Energy (3) Displacement (4) Force (5) Work
(6) Pressure (7) Torque (8) Weight (9) Velocity

A1. Stress & Force, Energy & Work, Force & Weight




Q2 In the above question, Select the odd one ? Write the uses of dimensional analysis ?

A2. odd one is Torque because it is related to circular motion.

Uses of dimensional analysis are

I. Check the correctness of an equation
II. Derive an equation relating to two or three physical quantities
III. Find dimension of constants in an equation
IV. Convert unit from one system to another.

Motion in one dimension

Q1. A balloon raises with constant velocity 10 m/s. A load tied by a rope to the balloon is cut when it is at a height of 500 m.
(a) How long will it take to reach the ground ?

A1.

Here Initial velocity u = 10 m/s ( Positive , since direction of initial motion is positive)

Displacement , S = - 500 m (towards downward - against initial motion direction)

Acceleration (due to gravity) , a = - 9.8 m/s2 (also downwards - against initial motion direction)

Use equations: S = ut + 1/2 a t2

See answer as : t = 11.12 seconds

Thursday, March 17, 2011

Vector sum



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