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 to a point other than $(0,0)$,find the correct dimensions of $A$ and $B$ in the new equation: $(x-At)^2+(y-\frac{t}{B})^2=a^2$. The dimensions of $t$ are given as $[T^{-1}]$.
- A$A=[L^{-1}T], B=[LT^{-1}]$
- B$A=[LT], B=[L^{-1}T^{-1}]$
- C$A=[L^{-1}T^{-1}], B=[LT^{-1}]$
- D$A=[L^{-1}T^{-1}], B=[LT]$
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List-$I$ List-$II$ $A$. Meter $(L)$ $I$. $\sqrt{\frac{hc}{G}}$ $B$. Second $(S)$ $II$. $\sqrt{\frac{Gh}{c^5}}$ $C$. Kilogram $(M)$ $III$. $\sqrt{\frac{L^2c^3}{Gh}}$ $D$. Kelvin $(K)$ $IV$. $\sqrt{\frac{Gh}{c^3}}$
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| $D$. Kelvin $(K)$ | $IV$. $\sqrt{\frac{Gh}{c^3}}$ |
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