Question 168: 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: