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In the formula X =5YZ^(2), X and Z have ...

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?

A

`[M^(-2) L^(0) T^(-4) A^(-2)]`

B

`[M^(-3) L^(-2) T^(8) A^(4)]`

C

`[M^(-2) L^(-2) T^(6) A^(3)]`

D

`[M^(-1) L^(-2) T^(4) A^(2)]`

Text Solution

Verified by Experts

The correct Answer is:
B
`Y=(X)/(2Z^2)=(Q/V)/(2 xx(F/(Qv)))=(Q^2v^2)/(2VF^2)`
`Y=(A^3 T^3xxL^2 xxT^(-2))/(2((ML^2T^(-2))/(AT))xxM^2 L^2 T^(-4))`
`Y=[M^(-3)L^(-2)T^(4)Q^(4)]and Q=AT`
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