Question
Download Solution PDFWhich of following is the dimensional formula of Density?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- The dimensional formula is defined as the expression of the physical quantity in terms of mass, length, time, and ampere.
EXPLANATION:
- Density: It is defined as mass per unit volume.
i.e. \(Density = \frac{{Mass}}{{Volume}}\)
Now,
Dimensional formula of mass = [M]
Dimensional formula of volume = [L3]
\(Density = \frac{{\left[ M \right]}}{{\left[ {{L^3}} \right]}}\)
∴ Density = ML-3 T0
∴ Dimensional formula of density is [ML-3 T0].
- Some Basic Dimensional formula:
|
Sl. No. |
Quantity |
Common Symbol |
SI Unit |
Dimension |
|
1 |
Velocity |
v, u |
ms-1 |
LT-1 |
|
2 |
Acceleration |
a |
ms-2 |
LT-2 |
|
3 |
Force |
F |
Newton (N) |
M L T-2 |
|
4 |
Momentum |
p |
Kg-ms-1 |
M L T-1 |
|
5 |
Gravitational constant |
G |
N-m2Kg-2 |
L3 M-1 T-2 |
|
6 |
Torque |
τ |
N-m |
M L2 T-2 |
|
7 |
Bulk Modulus |
B |
Nm2 |
M L-1 T-2 |
|
8 |
Energy |
E, U, K |
joule (J) |
M L2 T-2 |
|
9 |
Heat |
Q |
joule (J) |
M L2 T-2 |
|
10 |
Pressure |
P |
Nm-2 (Pa) |
M L-1 T-2 |
|
11 |
Electric Field |
E |
Vm-1, NC-1 |
M L I-1 T-3 |
|
12 |
Potential (voltage) |
V |
V, JC-1 |
M L2 I-1 T-3 |
|
13 |
Magnetic Field |
B |
Tesla (T), Wb m-1 |
M I-1T-2 |
|
14 |
Magnetic Flux |
ΦB |
Wb |
M L2 I-1 T-2 |
|
15 |
Resistance |
R |
Ohm (Ω) |
M L2 I-2 T-3 |
|
16 |
Electromotive Force |
E |
Volt (V) |
M L2 I-1 T-3 |
| 17 | Density | ρ, d | kg/m3 | ML-3 T0 |
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