a) State the principle of homogeneity. (1)
b) Using this principle, check whether the following equation is dimensionally correct. ½ mv2 = mgh ,
Where m is the mass of the body, v is its velocity, g is the acceleration due to gravity and h is the heigh
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Answered by
0
Answer: =
GM
4π
2
r
3
Taking dimensions on both sides, we get
[T]
2
=
[M
−1
L
3
T
−2
M]
[L]
3
=[M
0
L
0
T
2
]
∴LHS=RHS
Now, T
2
=4π
2
r
2
Taking dimensions on both sides
[T]
2
=[L]
2
∴LHS
=RHS
Now, T
2
=
G
4π
2
r
3
Taking dimensions on both sides
[T]
2
=
[M
−1
L
3
T
2
]
[L]
3
=[M
1
L
0
T
−2
] ∴LHS
=RHS
Now, T=
G
4π
2
r
3
[T]=
[M
−1
L
3
T
−2
]
[L]
3
=[ML
0
T
2
] ∴LHS
=RHS
Answered by
0
Answer:
- Homogeneity Principle of Dimensional Analysis
- Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same. This principle is helpful because it helps us convert the units from one form to another .
- We know ForceF=mass×acceleration----------(1)
- And given ForceF=
- r
- mv
- 2
- ----------(2)
- Equating 1 and 2 dimensionaly we get ,
- ma=
- r
- mv
- 2
- MLT
- −2
- =ML
- 2
- T
- −2
- L
- −1
- MLT
- −2
- =MLT
- −2
Explanation:
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