devarshi-dt-logo

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?

[M⁻¹L⁻²T⁴A²]

[M⁻²L⁻²T⁶A³]

[M⁻³L⁻²T⁸A⁴]

[M⁻²L⁰T⁻⁴A⁻²]

Solution:

Correct option is C. [M⁻³L⁻²T⁸A⁴]
X = 5YZ²
Y = X/(5Z²)
[Y] = [X]/[Z²]
[X] = Dimensions of Capacitance = A²M⁻¹L⁻²T⁴
[Z] = Dimensions of Magnetic Field = MT⁻²A⁻¹
[Y] = (A²M⁻¹L⁻²T⁴)/(MT⁻²A⁻¹)²
= A²M⁻¹L⁻²T⁴/(M²T⁻⁴A⁻²)
= M⁻³L⁻²T⁸A⁴