Q27. The potential energy V of a particle varies with its distance x from a fixed origin according to V = A√x /(x+B), where A and B are constants having appropriate dimensions. What are the dimensions of the product AB?
Options

Question

Q27. The potential energy V of a particle varies with its distance x from a fixed origin according to V = A√x /(x+B), where A and B are constants having appropriate dimensions. What are the dimensions of the product AB?

Options

G1 Physics · Accepted Answer

Because x and B are added in the denominator, [B] = [x] = L. Potential energy has dimensions [V] = M L² T⁻². From V = A√x ÷ (x+B), the dimensional relation is M L² T⁻² = [A]L¹⁄² ÷ L. Hence, [A] = M L⁵⁄² T⁻². Therefore, [AB] = [A][B] = M L⁵⁄² T⁻² × L = M L⁷⁄² T⁻². Correct option: D.