JEE Physics 2023 Question with Solution

Given:

• The circle equation is

$$(x - At)^2 + \left(y - \frac{t}{B}\right)^2 = a^2$$

• $x$, $y$, and $a$ have dimensions of length, that is $[L]$.
• $t$ has dimensions $[T^{-1}]$.

Find: The dimensions of $A$ and $B$.

For dimensional consistency, each term being subtracted from $x$ and $y$ must also have dimensions of length.

From the first bracket:

$$[At] = [L]$$

So,

$$[A] = \frac{[L]}{[T^{-1}]} = [LT]$$

From the second bracket:

$$\left[\frac{t}{B}\right] = [L]$$

So,

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

Therefore, the correct dimensions are $A = [LT]$ and $B = [L^{-1}T^{-1}]$. The correct option is B.