Question 196: Units , Dimensions and Error Analysis

Question

In the formula X = 5YZ
2
, X and Z have dimensions of capacitance and magnetic field, respectively. What are
the dimensions of Y in SI units?

Accepted Answer

Capacitance (C) = ${{{Q^2}} \over {2E}}$ = ${{\left[ {{A^2}{T^2}} ight]} \over {\left[ {M{L^2}{T^{ - 2}}} ight]}}$ = $\left[ {{M^{ - 1}}{L^{ - 2}}{T^4}{A^2}} ight]$ X
Magnetic field (B) = ${F \over {IL}}$ = ${{\left[ {ML{T^{ - 2}}} ight]} \over {\left[ A ight]\left[ L ight]}}$ = ${\left[ {M{T^{ - 2}}{A^{ - 1}}} ight]}$ = Z
Given,
X = 5YZ
2
$ 	herefore $ Y = ${X \over {5{Z^2}}}$
[Y] = ${{\left[ {{M^{ - 1}}{L^{ - 2}}{T^4}{A^2}} ight]} \over {{{\left[ {M{T^{ - 2}}{A^{ - 1}}} ight]}^2}}}$
$ 	herefore $ [Y] =  [M
Ã¢ÂÂ3
L
Ã¢ÂÂ2
T
8
A
4
]

Answer

[M
–3
L
–2
T
8
A
4
]

Answer

[M
–2
L
–2
T
6
A
3
]

Answer

[M
–1
L
–2
T
4
A
2
]

Answer

[M
–2
L
0
T
–4
A
–2
]

Units , Dimensions and Error Analysis

In the formula X = 5YZ 2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

Choose the correct answer: