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: \((x-A t)^2+\left(y-\frac{t}{B}\right)^2=a^2\).The dimensions of \(t\) is given as \(\left[ T ^{-1}\right]\).

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Answer & Solution

Correct Answer

(B) \(A =[ LT ], B =\left[ L ^{-1} T ^{-1}\right]\)

Detailed explanation

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

\({[ At ]= A \times \frac{1}{ T }= L }\)

\(\therefore \quad[ A ]= T ^1 L ^1\)

\(\quad \frac{ t }{ B } \text { is in meters }\)

\(\therefore \quad \frac{1}{ T [ B ]}= L\)

\(\therefore \quad[ B ]= T ^{-1} L ^{-1}\)

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