Cheat Sheet: Units & Measurements | Physics Class 11 - NEET PDF Download

 Page 1


UnitsandMeasurements
CheatSheet
Fundamental and Derived Quantities
Type Description Examples
Fundamental Basic quantities independent of others. Length (m), Mass (kg), Time
(s)
Derived Quantities derived from fundamental
quantities using mathematical relations.
Velocity (m/s), Force
(kg·m/s
2
), Energy (J)
SI Units
Quantity Unit Symbol
Length Meter m
Mass Kilogram kg
Time Second s
Electric Current Ampere A
Temperature Kelvin K
Amount of Substance Mole mol
Luminous Intensity Candela cd
Dimensional Analysis
• De?nition: Technique to check equation consistency using dimensions of physical quantities.
• Key Formula: [M
a
L
b
T
c
], where M = mass, L = length, T = time.
• Applications:
– Verify formula correctness.
– Derive relations between physical quantities.
– Convert units across systems (e.g., SI to CGS).
Signi?cant Figures
• Rules:
– Non-zero digits are always signi?cant.
– Zeros between non-zero digits are signi?cant.
– Leading zeros are not signi?cant.
– Trailing zeros in a decimal are signi?cant.
• Operations:
1
Page 2


UnitsandMeasurements
CheatSheet
Fundamental and Derived Quantities
Type Description Examples
Fundamental Basic quantities independent of others. Length (m), Mass (kg), Time
(s)
Derived Quantities derived from fundamental
quantities using mathematical relations.
Velocity (m/s), Force
(kg·m/s
2
), Energy (J)
SI Units
Quantity Unit Symbol
Length Meter m
Mass Kilogram kg
Time Second s
Electric Current Ampere A
Temperature Kelvin K
Amount of Substance Mole mol
Luminous Intensity Candela cd
Dimensional Analysis
• De?nition: Technique to check equation consistency using dimensions of physical quantities.
• Key Formula: [M
a
L
b
T
c
], where M = mass, L = length, T = time.
• Applications:
– Verify formula correctness.
– Derive relations between physical quantities.
– Convert units across systems (e.g., SI to CGS).
Signi?cant Figures
• Rules:
– Non-zero digits are always signi?cant.
– Zeros between non-zero digits are signi?cant.
– Leading zeros are not signi?cant.
– Trailing zeros in a decimal are signi?cant.
• Operations:
1
– Addition/Subtraction: Result has same decimal places as the number with the least decimal
places.
– Multiplication/Division: Result has same signi?cant ?gures as the number with the least sig-
ni?cant ?gures.
Errors in Measurement
Type Description Formula
Absolute Error Di?erence between measured and true
value.
? a =|a
m
-a
t
|
Relative Error Ratio of absolute error to true value. da = ? a/a
t
Percentage Error Relative error expressed as a percentage. % Error = (? a/a
t
)×100
Combination of Er-
rors
For a function Z =A
m
B
n
/C
p
: ? Z/Z = m(? A/A) +
n(? B/B)+p(? C/C)
Measurement Techniques
Instrument Purpose Precision (Least Count)
Vernier Caliper Measures length, diameter,
thickness.
LC=1MSD-1VSD(typically0.01
cm)
Screw Gauge Measures small dimensions
(e.g., wire).
LC = Pitch / No. of divisions (e.g.,
0.001 cm)
Stopwatch Measures time intervals. Typically 0.01 s
Conversion of Units
• Length: 1 m = 100 cm = 10
9
nm; 1 km = 0.621 miles.
• Mass: 1 kg = 1000 g; 1 tonne = 1000 kg.
• Time: 1 hr = 3600 s; 1 year ˜ 3.156×10
7
s.
• Energy: 1 J = 10
7
erg; 1 eV = 1.602×10
-19
J.
• Pressure: 1 Pa = 1 N/m
2
; 1 atm = 101325 Pa.
Key Formulas and Concepts
• Density: ? =m/V (kg/m
3
)
• Speed: v =d/t (m/s)
• Acceleration: a = ? v/? t (m/s
2
)
• Order of Magnitude: Approximate value to the nearest power of 10.
• Parallax Error: Error due to improper alignment of observers eye with the measurement scale.
Solved Examples
1. Dimensional Analysis: Derive the dimensional formula for viscosity (?) in the formula F =
?A(v/l), where F is force, A is area, v is velocity, and l is length.
• Solution:
– Dimensions of F = [MLT
-2
], A = [L
2
], v = [LT
-1
], l = [L].
2
Page 3


UnitsandMeasurements
CheatSheet
Fundamental and Derived Quantities
Type Description Examples
Fundamental Basic quantities independent of others. Length (m), Mass (kg), Time
(s)
Derived Quantities derived from fundamental
quantities using mathematical relations.
Velocity (m/s), Force
(kg·m/s
2
), Energy (J)
SI Units
Quantity Unit Symbol
Length Meter m
Mass Kilogram kg
Time Second s
Electric Current Ampere A
Temperature Kelvin K
Amount of Substance Mole mol
Luminous Intensity Candela cd
Dimensional Analysis
• De?nition: Technique to check equation consistency using dimensions of physical quantities.
• Key Formula: [M
a
L
b
T
c
], where M = mass, L = length, T = time.
• Applications:
– Verify formula correctness.
– Derive relations between physical quantities.
– Convert units across systems (e.g., SI to CGS).
Signi?cant Figures
• Rules:
– Non-zero digits are always signi?cant.
– Zeros between non-zero digits are signi?cant.
– Leading zeros are not signi?cant.
– Trailing zeros in a decimal are signi?cant.
• Operations:
1
– Addition/Subtraction: Result has same decimal places as the number with the least decimal
places.
– Multiplication/Division: Result has same signi?cant ?gures as the number with the least sig-
ni?cant ?gures.
Errors in Measurement
Type Description Formula
Absolute Error Di?erence between measured and true
value.
? a =|a
m
-a
t
|
Relative Error Ratio of absolute error to true value. da = ? a/a
t
Percentage Error Relative error expressed as a percentage. % Error = (? a/a
t
)×100
Combination of Er-
rors
For a function Z =A
m
B
n
/C
p
: ? Z/Z = m(? A/A) +
n(? B/B)+p(? C/C)
Measurement Techniques
Instrument Purpose Precision (Least Count)
Vernier Caliper Measures length, diameter,
thickness.
LC=1MSD-1VSD(typically0.01
cm)
Screw Gauge Measures small dimensions
(e.g., wire).
LC = Pitch / No. of divisions (e.g.,
0.001 cm)
Stopwatch Measures time intervals. Typically 0.01 s
Conversion of Units
• Length: 1 m = 100 cm = 10
9
nm; 1 km = 0.621 miles.
• Mass: 1 kg = 1000 g; 1 tonne = 1000 kg.
• Time: 1 hr = 3600 s; 1 year ˜ 3.156×10
7
s.
• Energy: 1 J = 10
7
erg; 1 eV = 1.602×10
-19
J.
• Pressure: 1 Pa = 1 N/m
2
; 1 atm = 101325 Pa.
Key Formulas and Concepts
• Density: ? =m/V (kg/m
3
)
• Speed: v =d/t (m/s)
• Acceleration: a = ? v/? t (m/s
2
)
• Order of Magnitude: Approximate value to the nearest power of 10.
• Parallax Error: Error due to improper alignment of observers eye with the measurement scale.
Solved Examples
1. Dimensional Analysis: Derive the dimensional formula for viscosity (?) in the formula F =
?A(v/l), where F is force, A is area, v is velocity, and l is length.
• Solution:
– Dimensions of F = [MLT
-2
], A = [L
2
], v = [LT
-1
], l = [L].
2
– F =?A(v/l)? [MLT
-2
] =?[L
2
]([LT
-1
]/[L]) =?[L
2
][T
-1
].
– ? = [MLT
-2
]/[L
2
T
-1
] = [ML
-1
T
-1
].
– Answer: [ML
-1
T
-1
].
2. ErrorPropagation: Theradiusofasphereismeasuredas 7.00±0.02cm. Calculatethepercentage
error in its volume.
• Solution:
– Volume of sphere, V = (4/3)pr
3
, so ? V/V = 3(? r/r).
– Given r = 7.00 cm, ? r = 0.02 cm.
– Relative error = ? r/r = 0.02/7.00 = 0.002857.
– Percentage error in volume = 3×0.002857×100 = 0.857%.
– Answer: 0.86% (to 2 signi?cant ?gures).
3. Signi?cant Figures: Calculate the area of a rectangle with length 12.4 cm and breadth 3.567 cm,
expressing the result with appropriate signi?cant ?gures.
• Solution:
– Area = length × breadth = 12.4×3.567 = 44.2308 cm
2
.
– Lengthhas3signi?cant?gures, breadthhas4; resultshouldhave3signi?cant?gures(least
of the two).
– Round 44.2308 to 44.2 cm
2
.
– Answer: 44.2 cm
2
.
4. Vernier Caliper: A vernier caliper has a main scale division (MSD) of 1 mm and 10 vernier
divisions coincide with 9 main scale divisions. Find its least count and measure a length of 5.3 cm
with an error.
• Solution:
– Least count (LC) = 1 MSD - 1 VSD, where 10 VSD = 9 MSD ? 1 VSD = 0.9 mm.
– LC = 1 mm - 0.9 mm = 0.1 mm = 0.01 cm.
– Measured length = 5.3 cm ± 0.01 cm (error is ± LC).
– Answer: Least count = 0.01 cm, length = 5.3±0.01 cm.
5. Unit Conversion: A cars speed is 72 km/h. Convert this to cm/s and determine the order of
magnitude.
• Solution:
– 72 km/h = 72×1000 m / 3600 s = 72×1000/3600 = 20 m/s.
– 20 m/s = 20×100 cm/s = 2000 cm/s.
– Order of magnitude: 2000 = 2×10
3
? order of magnitude is 10
3
.
– Answer: 2000 cm/s, order of magnitude = 10
3
.
3