Important Physics and measurement Formulas for JEE and NEET

 Page 1


UNIT AND DIMENSIONS
Unit :
Measurement of any physical quantity is expressed in terms of an
internationally accepted certain basic standard called unit.
* Fundamental Units.
S.No. Physical Quantity SI Unit Symbol 
1 Length Metre m  
2 Mass Kilogram Kg 
3 Time Second S 
4 Electric Current Ampere A 
5 Temperature Kelvin K 
6 Luminous Intensity Candela Cd 
7 Amount of Substance Mole mol 
 
* Supplementary Units :
S.No. Physical Quantity SI Unit Symbol 
1 Plane Angle radian r 
2 Solid Angle  Steradian Sr 
 
* Metric Prefixes :
 
S.No. Prefix Sym bol Value 
1 Centi c  10
–2
 
2 M ili  m  10
–3
 
3 M icro µ 10
–6
 
4 Nano n  10
–9
 
5 Pico p  10
–12
 
6 Kilo K 10
3
 
7 M ega M 10
6
 
 
Page 2


UNIT AND DIMENSIONS
Unit :
Measurement of any physical quantity is expressed in terms of an
internationally accepted certain basic standard called unit.
* Fundamental Units.
S.No. Physical Quantity SI Unit Symbol 
1 Length Metre m  
2 Mass Kilogram Kg 
3 Time Second S 
4 Electric Current Ampere A 
5 Temperature Kelvin K 
6 Luminous Intensity Candela Cd 
7 Amount of Substance Mole mol 
 
* Supplementary Units :
S.No. Physical Quantity SI Unit Symbol 
1 Plane Angle radian r 
2 Solid Angle  Steradian Sr 
 
* Metric Prefixes :
 
S.No. Prefix Sym bol Value 
1 Centi c  10
–2
 
2 M ili  m  10
–3
 
3 M icro µ 10
–6
 
4 Nano n  10
–9
 
5 Pico p  10
–12
 
6 Kilo K 10
3
 
7 M ega M 10
6
 
 
 
 
 
  
  
 
 
  
 
 
  
 
 
 
 
 
 
  
 
 
  
  
 
 
 
 
ERROR AND MEASUREMENT
1. Least Count
 
 
mm.scale 
L.C =1mm
Vernier 
L.C=0.1mm
Screw gauge 
L.C=0.1mm 
Stop Watch 
L.C=0.1Sec 
Temp thermometer
L.C=0.1°C 
2. Significant Figures
? Non-zero digits are significant
? Zeros occurring between two non-zeros digits are significant.
? Change of units cannot change S.F.
? In the number less than one, all zeros after decimal point and to
the left of first non-zero digit are insignificant
? The terminal or trailing zeros in a number without a decimal
point are not significant.
Page 3


UNIT AND DIMENSIONS
Unit :
Measurement of any physical quantity is expressed in terms of an
internationally accepted certain basic standard called unit.
* Fundamental Units.
S.No. Physical Quantity SI Unit Symbol 
1 Length Metre m  
2 Mass Kilogram Kg 
3 Time Second S 
4 Electric Current Ampere A 
5 Temperature Kelvin K 
6 Luminous Intensity Candela Cd 
7 Amount of Substance Mole mol 
 
* Supplementary Units :
S.No. Physical Quantity SI Unit Symbol 
1 Plane Angle radian r 
2 Solid Angle  Steradian Sr 
 
* Metric Prefixes :
 
S.No. Prefix Sym bol Value 
1 Centi c  10
–2
 
2 M ili  m  10
–3
 
3 M icro µ 10
–6
 
4 Nano n  10
–9
 
5 Pico p  10
–12
 
6 Kilo K 10
3
 
7 M ega M 10
6
 
 
 
 
 
  
  
 
 
  
 
 
  
 
 
 
 
 
 
  
 
 
  
  
 
 
 
 
ERROR AND MEASUREMENT
1. Least Count
 
 
mm.scale 
L.C =1mm
Vernier 
L.C=0.1mm
Screw gauge 
L.C=0.1mm 
Stop Watch 
L.C=0.1Sec 
Temp thermometer
L.C=0.1°C 
2. Significant Figures
? Non-zero digits are significant
? Zeros occurring between two non-zeros digits are significant.
? Change of units cannot change S.F.
? In the number less than one, all zeros after decimal point and to
the left of first non-zero digit are insignificant
? The terminal or trailing zeros in a number without a decimal
point are not significant.
3. Permissible Error
? Max permissible error in a measured quantity = least count of
the measuring instrument and if nothing is given about least count
then Max permissible error = place value of the last number
? f (x,y) = x + y     then   ( ?f)
max
 = max of ( ? ?X ? ?Y)
? ?f (x,y,z) = (constant) x
a
 y
b
 z
c
  then
max
f
f
?
?
?
?
?
? ?
= max of  ?
?
?
?
?
?
?
? ?
?
?
?
?
?
z
z
c
y
y
b
x
x
a
4. Errors in averaging
? Absolute Error   ?a
n
 = |a
mean
 -a
n
|
? Mean Absolute Error ?a
mean
 =   
n
| a |
n
1 i
i
?
?
?
?
?
?
?
?
?
?
?
? Relative error =  
mean
mean
a
a ?
? Percentage error = 
mean
mean
a
a ?
×100
5. Experiments
? Reading of screw gauge
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
count
Least
reading
scale
circular
reading
scale
main
gauge screw of ading Re object of Thicknes
 least count of screw gauge =
division scale circular of . No
pitch
? Vernier callipers
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
count
Least
reading
scale
vernier
reading
scale
main
calliper vernier of ading Re object of Thicknes
Least count of vernier calliper = 1 MSD –1 VSD
Page 4


UNIT AND DIMENSIONS
Unit :
Measurement of any physical quantity is expressed in terms of an
internationally accepted certain basic standard called unit.
* Fundamental Units.
S.No. Physical Quantity SI Unit Symbol 
1 Length Metre m  
2 Mass Kilogram Kg 
3 Time Second S 
4 Electric Current Ampere A 
5 Temperature Kelvin K 
6 Luminous Intensity Candela Cd 
7 Amount of Substance Mole mol 
 
* Supplementary Units :
S.No. Physical Quantity SI Unit Symbol 
1 Plane Angle radian r 
2 Solid Angle  Steradian Sr 
 
* Metric Prefixes :
 
S.No. Prefix Sym bol Value 
1 Centi c  10
–2
 
2 M ili  m  10
–3
 
3 M icro µ 10
–6
 
4 Nano n  10
–9
 
5 Pico p  10
–12
 
6 Kilo K 10
3
 
7 M ega M 10
6
 
 
 
 
 
  
  
 
 
  
 
 
  
 
 
 
 
 
 
  
 
 
  
  
 
 
 
 
ERROR AND MEASUREMENT
1. Least Count
 
 
mm.scale 
L.C =1mm
Vernier 
L.C=0.1mm
Screw gauge 
L.C=0.1mm 
Stop Watch 
L.C=0.1Sec 
Temp thermometer
L.C=0.1°C 
2. Significant Figures
? Non-zero digits are significant
? Zeros occurring between two non-zeros digits are significant.
? Change of units cannot change S.F.
? In the number less than one, all zeros after decimal point and to
the left of first non-zero digit are insignificant
? The terminal or trailing zeros in a number without a decimal
point are not significant.
3. Permissible Error
? Max permissible error in a measured quantity = least count of
the measuring instrument and if nothing is given about least count
then Max permissible error = place value of the last number
? f (x,y) = x + y     then   ( ?f)
max
 = max of ( ? ?X ? ?Y)
? ?f (x,y,z) = (constant) x
a
 y
b
 z
c
  then
max
f
f
?
?
?
?
?
? ?
= max of  ?
?
?
?
?
?
?
? ?
?
?
?
?
?
z
z
c
y
y
b
x
x
a
4. Errors in averaging
? Absolute Error   ?a
n
 = |a
mean
 -a
n
|
? Mean Absolute Error ?a
mean
 =   
n
| a |
n
1 i
i
?
?
?
?
?
?
?
?
?
?
?
? Relative error =  
mean
mean
a
a ?
? Percentage error = 
mean
mean
a
a ?
×100
5. Experiments
? Reading of screw gauge
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
count
Least
reading
scale
circular
reading
scale
main
gauge screw of ading Re object of Thicknes
 least count of screw gauge =
division scale circular of . No
pitch
? Vernier callipers
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
count
Least
reading
scale
vernier
reading
scale
main
calliper vernier of ading Re object of Thicknes
Least count of vernier calliper = 1 MSD –1 VSD
Page 5


UNIT AND DIMENSIONS
Unit :
Measurement of any physical quantity is expressed in terms of an
internationally accepted certain basic standard called unit.
* Fundamental Units.
S.No. Physical Quantity SI Unit Symbol 
1 Length Metre m  
2 Mass Kilogram Kg 
3 Time Second S 
4 Electric Current Ampere A 
5 Temperature Kelvin K 
6 Luminous Intensity Candela Cd 
7 Amount of Substance Mole mol 
 
* Supplementary Units :
S.No. Physical Quantity SI Unit Symbol 
1 Plane Angle radian r 
2 Solid Angle  Steradian Sr 
 
* Metric Prefixes :
 
S.No. Prefix Sym bol Value 
1 Centi c  10
–2
 
2 M ili  m  10
–3
 
3 M icro µ 10
–6
 
4 Nano n  10
–9
 
5 Pico p  10
–12
 
6 Kilo K 10
3
 
7 M ega M 10
6
 
 
 
 
 
  
  
 
 
  
 
 
  
 
 
 
 
 
 
  
 
 
  
  
 
 
 
 
ERROR AND MEASUREMENT
1. Least Count
 
 
mm.scale 
L.C =1mm
Vernier 
L.C=0.1mm
Screw gauge 
L.C=0.1mm 
Stop Watch 
L.C=0.1Sec 
Temp thermometer
L.C=0.1°C 
2. Significant Figures
? Non-zero digits are significant
? Zeros occurring between two non-zeros digits are significant.
? Change of units cannot change S.F.
? In the number less than one, all zeros after decimal point and to
the left of first non-zero digit are insignificant
? The terminal or trailing zeros in a number without a decimal
point are not significant.
3. Permissible Error
? Max permissible error in a measured quantity = least count of
the measuring instrument and if nothing is given about least count
then Max permissible error = place value of the last number
? f (x,y) = x + y     then   ( ?f)
max
 = max of ( ? ?X ? ?Y)
? ?f (x,y,z) = (constant) x
a
 y
b
 z
c
  then
max
f
f
?
?
?
?
?
? ?
= max of  ?
?
?
?
?
?
?
? ?
?
?
?
?
?
z
z
c
y
y
b
x
x
a
4. Errors in averaging
? Absolute Error   ?a
n
 = |a
mean
 -a
n
|
? Mean Absolute Error ?a
mean
 =   
n
| a |
n
1 i
i
?
?
?
?
?
?
?
?
?
?
?
? Relative error =  
mean
mean
a
a ?
? Percentage error = 
mean
mean
a
a ?
×100
5. Experiments
? Reading of screw gauge
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
count
Least
reading
scale
circular
reading
scale
main
gauge screw of ading Re object of Thicknes
 least count of screw gauge =
division scale circular of . No
pitch
? Vernier callipers
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
count
Least
reading
scale
vernier
reading
scale
main
calliper vernier of ading Re object of Thicknes
Least count of vernier calliper = 1 MSD –1 VSD