Question

The formula X = 5YZ² X and Z have dimensions of capacitance and magnetic field respectively. What are the dimensions of Y in SI units?
(A) [M⁻² L⁰ T⁻⁴ A⁻²
] (B) [M⁻³ L⁻² T⁸ A⁻¹
]
(C) [M⁻² L⁻² T⁶ A³
] (D) [M⁻¹ L⁻² T⁴ A²
]

Answer 1

The dimensions of Y in SI units is :

M⁻³.L⁻².T⁸.A⁴

The dimension can be found out in the following ways-

Given,  X = 5YZ² , therefore,

• X = 5YZ²

• Y = X / 5Z²​

• [Y] = [X] [Z²]​

• [Y] = (A².M⁻¹L⁻².T⁴) / (MA⁻¹T⁻²)²

• [Y] = M⁻³.L⁻².T⁸.A⁴

Thus, the dimension of Y in SI unit is  M⁻³.L⁻².T⁸.A⁴.