Question 190: Units , Dimensions and Error Analysis

Question

Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimensions of mass would be :

Accepted Answer

Let,
M $$ \propto $$ T
x
C
y
h
z
$$	herefore\,\,\,$$ [M
1
L
o
T
o
]  =  [T
1
]
x
[L
1
T
$$-$$1
]
y
[M
1
L
2
T
$$-$$1
]
z
[M
1
L
o
T
o
]   =  [M
z
L
y + 2z
T
x$$-$$y$$-$$z
]
By comparing both sides we get,
z = 1
y + 2z = 0
x $$-$$ y $$-$$ z = 0
$$	herefore\,\,\,$$ y = $$-$$ 2z = $$-$$ 2
x = y + z = $$-$$2 + 1 = $$-$$1
$$	herefore\,\,\,$$ [M] = [M
$$-$$1
C
$$-$$2
h
1
]

Answer

[M] = [T
$$-$$1
C
$$-$$2
h]

Answer

[M] = [T
$$-$$1
C
2
h]

Answer

[M] = [T
$$-$$1
C
$$-$$2
h
$$-$$1
]

Answer

[M] = [T C
$$-$$2
h]

Units , Dimensions and Error Analysis

Time (T), velocity (C) and angular momentum (h) are chosen as fundamentalquantities instead of mass, length and time. In terms of these, the dimensions of mass would be :

Choose the correct answer: