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The potential energy of a particle varies the distance x from a fixed origin as U=(Asqrtx)/(X^(2)+B), where A and B are dimensional constants, then find the dimensional formula for AB.^(2)

The potential energy of a particle varies the distance xx from a fixed origin as U=AxX2+BU=\frac{A\sqrt{x}}{X^{2}+B}, where AA and BB are dimensional constants, then find the dimensional formula for AB2AB^{2}.

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Full solution

Q. The potential energy of a particle varies the distance xx from a fixed origin as U=AxX2+BU=\frac{A\sqrt{x}}{X^{2}+B}, where AA and BB are dimensional constants, then find the dimensional formula for AB2AB^{2}.
  1. Identify dimensions: Identify the dimensions of each term in the equation U=Axx2+BU = \frac{A\sqrt{x}}{x^2 + B}.
  2. Set up equation: Set up the dimensional equation for UU based on the given formula.
  3. Simplify for [A][A]: Simplify the dimensional equation to find [A][A].
  4. Calculate AB2AB^2 dimensions: Calculate the dimensions of AB2AB^2.

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