JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Units & Measurement

The formula

X = 5 Y Z^{2}

X

and

Z

have dimensions of capacitance and magnetic field respectively. What are the dimensions of Y in SI units?

Answer: (B)

Solution

Capacitance has dimensions

[M^{- 1} L^{- 2} T^{4} A^{2}]

and magnetic field has dimensions

[M T^{- 2} A^{- 1}]

. In

X = 5 Y Z^{2}

the factor

5

is a pure number, so dimensionally

[Y] = \frac{[ X ]}{[ Z ] ^{2}}

. Substituting,

[Y] = \frac{[ M ^{- 1} L ^{- 2} T ^{4} A ^{2} ]}{[ M T ^{- 2} A ^{- 1} ] ^{2}} = \frac{[ M ^{- 1} L ^{- 2} T ^{4} A ^{2} ]}{[ M ^{2} T ^{- 4} A ^{- 2} ]}

. Subtracting the exponents,

[Y] = M^{- 1 - 2} L^{- 2} T^{4 - (- 4)} A^{2 - (- 2)} = M^{- 3} L^{- 2} T^{8} A^{4}

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option