Q 11-01-128JEE MainJEE Main 2023 (29 Jan, Shift 2)Medium
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:
$$(x-At)^2+\left(y-\frac{t}{B}\right)^2=a^2$$
The dimensions of $t$ is given as $[\text{T}^{-1}]$.
Answer: (B) $A=[\text{L}\text{T}],\ B=[\text{L}^{-1}\text{T}^{-1}]$
Each term subtracted from a length must itself be a length.
$[At]=\text{L}\Rightarrow[A]=\dfrac{\text{L}}{\text{T}^{-1}}=[\text{L}\text{T}]$.
$\left[\dfrac{t}{B}\right]=\text{L}\Rightarrow[B]=\dfrac{\text{T}^{-1}}{\text{L}}=[\text{L}^{-1}\text{T}^{-1}]$.
Solution by Sreeraj P, M.Sc Physics