Question

In the fourmula X=3YZ^(2), X and Z have dimensions of capacitance and magnetic induction respectivey. What are the dimensions of Y is MKSQ system?

Answer 1

Answer:

answer : [M^-3 T^8 A^4 ]

Explanation:

In the formula, X = 3YZ² , X and Z have the dimensions of capacitance and magnetic induction.

we have to find dimension of Y in the mks system.

formula can be written as , Y = X/3Z²

from dimensional analysis,

or, dimension of Y = dimension of {X/3Z²}

= dimension of X/dimension of Z² [ as we know, numbers are dimensionless quantity so, 3 is dimensionless quantity.]

dimension of X = dimension of capacitance = [M-¹L-²T²Q²]

dimension of Z = dimension of magnetic induction = [MT-¹Q-¹]

so, dimension of Y = [M-¹L-²T²Q²]/[MT-¹Q-¹]²

= [M³ L-² T⁴ Q⁴ ]