JEE Main202329 Jan 2023Evening ShiftPhysicsUnits and DimensionsActual
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
Options
- AA   =   [ L – 1 T ] ,   B   =   [ LT – 1 ]
- BA = LT ,   B = [ L – 1 T   – 1 ]
- CA = [ L – 1 T   – 1   ] ,   B   =   [ LT – 1 ]  
- DA = [ L – 1 T   – 1 ] ,   B = [ LT ]  
Correct answer
B. A = LT ,   B = [ L – 1 T   – 1 ]
Step-by-step solution
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 - t B 2 = a 2 For first term, A t = x ⇒ A × 1 T = L ∴ A = T 1 L 1 For the second term, t B = y ⇒ 1 T B = L ⇒ B = T - 1 L - 1