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

Question

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 - t B 2 = a 2 The dimensions of t is given as T - 1

TestHub · Accepted Answer

Principle of Homogeneity states that dimensions of each of the terms of a dimensional equation on both sides should be the same. Then,

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

For first term,

$[A t] = [x] \Rightarrow A \times \frac{1}{T} = L$

$∴ [A] = T^{1} L^{1}$

For the second term,

$[\frac{t}{B}] = [y]$

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

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

Physics - Unit & Dimension Question with Solution | TestHub

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