Question

In the formula X = 3YZ², X and Z have dimensions of capacitance and magnetic induction respectively. The dimensions of Y in MKSA system are

• A. [M⁻3L⁻2T⁻4A⁻4]
• B. [ML⁻2]
• C. [M⁻3L⁻2A⁴T⁸]
• D. [M⁻3L²A⁴T⁴]

Hint:

Always write the given formula in dimensional form and isolate the required quantity before substituting dimensions.

Answer 1

The Correct Option is C

Step 1: Given relation: X = 3YZ² ⟹ [Y] = ([X])/([Z]²) Step 2: Dimensions: [X] = capacitance = [M⁻1L⁻2T⁴A²] [Z] = magnetic induction = [MT⁻2A⁻1] Step 3: Substitute: [Y] = fracM⁻1L⁻2T⁴A²M²T⁻4A⁻2 [Y] = M⁻3L⁻2T⁸A⁴