JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Units & Measurement

The equation of a circle is given by

x^{2} + y^{2} = a^{2}

, where a is the radius. If the equation is modified to change the origin other than

(0, 0)

, then find out the correct dimensions of A and B in a new equation:

(x - A t)^{2} + (y - \frac{t}{B})^{2} = a^{2}

.
The dimensions of

t

is given as

[T^{- 1}]

Answer: (B)

Solution

Each bracket that is squared must carry the dimension of length, matching

a

. For the term

A t

, with

[t] = [T^{- 1}]

, the requirement

[A] [T^{- 1}] = [L]

gives

[A] = [L T]

. For the term

t / B

, the requirement

\frac{[ T ^{- 1} ]}{[ B ]} = [L]

gives

[B] = [L^{- 1} T^{- 1}]

. Hence

A = [L T]

and

B = [L^{- 1} T^{- 1}]

JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Single correct option