Some Physical Quantities
S. No. |
Basic Physical Quantities |
Fundamental Unit |
Symbol |
1 |
Mass (M) |
kilogram |
kg |
2 |
Length (L) |
meter |
m |
3 |
Time (T) |
second |
s |
4 |
Temperature (\(\theta\)) |
kelvin |
k |
5 |
Electric Current (I) |
amphere |
A |
6 |
Luminous Intensity (cd) |
candela |
cd |
7 |
Quantity of matter (mol) |
mole |
mol |
Some Derived Units on SI
S. No. |
Physical Quantity |
Derived Unit |
Symbol |
1 |
Force |
Newton |
N |
2 |
Work, Energy |
Joule |
J |
3 |
Power |
Watt |
W |
4 |
Electric Potential |
Volt |
V |
5 |
Electric capacity |
Farad |
F |
6 |
Magnetic Flux |
Weber |
wb etc. |
Dimensional Formula and S.I. Units of Some Mechanical Quantities
S. No. |
Physical Quantity |
Relation with Other Quantity |
Dimensional Formula |
S.I. Unit |
1 |
Area |
Length \(\times\) Breadth |
L \(\times\) L = L^{2} = [M^{0}L^{2}T^{0}] |
m^{2} |
2 |
Volume |
Length \(\times\) Breadth \(\times\) Height |
L \(\times\) L \(\times\) L = L^{3} = [M^{0}L^{3}T^{0}] |
m^{3} |
3 |
Density |
\(\frac{\text{Mass}} {\text{Volume}}\) |
\(\frac{M}{L^3}\) = [M^{1}L^{-3}T^{0}] |
kgm^{-3} |
4 |
Velocity |
\(\frac{\text{Displacement}} {\text{Time}}\) |
\(\frac{L}{T}\) = [M^{0}L^{1}T^{-1}] |
ms^{-1} |
5 |
Linear Momentum |
Mass \(\times\) Velocity |
M \(\times\) LT^{-1} = [M^{1}L^{1}T^{-1}] |
kgms^{-1} |
6 |
Acceleration |
\(\frac{\text{Change in Velocity}}{\text{Time Taken}}\) |
\(\frac{\frac{L}{T}}{T}\) = [M^{0}L^{1}T^{-2}] |
ms^{-2} |
7 |
Acc. Due to gravity |
\(\frac{\text{Velocity}}{\text{Time}}\) |
\(\frac{\frac{L}{T}}{T}\) = [M^{0}L^{1}T^{-2}] |
ms^{-2} |
8 |
Force |
Mass \(\times\) Acceleration |
M \(\times\) LT^{-2} = [M^{1}L^{1}T^{-2}] |
N |
9 |
Pressure |
\(\frac{\text{Force}}{\text{Area}}\) |
\(\frac{MLT^{-2}}{L^2}\) = [M^{1}L^{-1}T^{-2}] |
Nm^{-2} |
10 |
Work |
Force \(\times\) Distance |
MLT^{-2} \(\times\) L = [M^{1}L^{2}T^{-2}] |
J |
11 |
Energy |
Force \(\times\) Distance |
MLT^{-2} \(\times\) L = [M^{1}L^{2}T^{-2}] |
J |
12 |
Power |
\(\frac{\text{Work}}{\text{Time}}\) |
\(\frac{ML^2T^{-2}} {T}\) = [M^{1}L^{2}T^{-3}] |
W |
13 |
Surface Tension |
\(\frac{\text{Force}}{\text{Length}}\) |
\(\frac{MLT^{-2}}{L}\) = [M^{1}L^{0}T^{-2}] |
Nm^{-1} |
14 |
Stress, Pressure |
\(\frac{\text{Force}}{\text{Area}}\) |
\(\frac{MLT^{-2}}{L^2}\) = [M^{1}L^{-1}T^{-2}] |
Nm^{-2} |
15 |
Strain |
\(\frac{\text{Change in Dimension}} {\text{Original Dimension}}\) |
\(\frac{L}{L}\) = 1 [M^{0}L^{0}T^{0}] |
No unit |
16 |
Torque |
Moment of Inertia \(\times\) Angular Acceleration |
ML^{2}(T^{-2}) = [M^{1}L^{2}T^{-2}] |
Nm |
17 |
Heat (Q) |
Energy |
[M^{1}L^{2}T^{-2}] |
J |
18 |
Latent Heat (L) |
\(\frac{\text{Heat(\(\theta\))}} {\text{Mass(m)}}\) |
\(\frac{ML^2T^{-2}}{M}\) = [M^{0}L^{2}T^{-2}] |
Jkg^{-1} |
Dimensions of More Physical Quantities
Dimension Analysis
Note
If any formula is dimensionally incorrect than the formula will be surely incorrect.
BUT
If a formula is dimensionally correct than it may be correct or incorrect.