The equation of a circle is x² + y² = a², 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 the new equation: (x - At)² + (y - t/B)² = a². The dimensions of t are given as [T⁻¹].
Options

Question

The equation of a circle is x² + y² = a², 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 the new equation: (x - At)² + (y - t/B)² = a². The dimensions of t are given as [T⁻¹].

Options

G1 Physics · Accepted Answer

Each term added to x or y must have dimensions of length. Since [t] = T⁻¹ and [At] = L, [A] = LT. Also [t/B] = L, so [B] = T⁻¹/L = L⁻¹T⁻¹. Hence option 2.