The potential energy of a particle changes with distance from a fixed origin as , where and are constant with appropriate dimensions

Question

The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \frac{A \sqrt{x}}{x + B}$ , where $A$ and $B$ are constant with appropriate dimensions. The dimension of $A B$ are ______. [2026]

Smart Achievers · Accepted Answer

(4)

$[B] = [x] = [L]$

$B$

$[A] = [M L^{5 / 2} T^{- 2}]$

$[A \cdot B] = [M L^{5 / 2} T^{- 2}] \times [L] = [M L^{7 / 2} T^{- 2}]$

Solution

Q.
The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \frac{A \sqrt{x}}{x + B}$ , where $A$ and $B$ are constant with appropriate dimensions. The dimension of $A B$ are ______. [2026]

1 $[M^{1} L^{5 / 2} T^{- 2}]$

2 $[M^{3 / 2} L^{5 / 2} T^{- 2}]$

3 $[M^{1} L^{2} T^{- 2}]$

4 $[M^{1} L^{7 / 2} T^{- 2}]$

Ans.
(4)

$[B] = [x] = [L]$

$[A] = \frac{[P E] \times [length]}{\sqrt{length}} = \frac{M L^{2} T^{- 2} \times L}{L^{1 / 2}}$

$[A] = [M L^{5 / 2} T^{- 2}]$

$[A \cdot B] = [M L^{5 / 2} T^{- 2}] \times [L] = [M L^{7 / 2} T^{- 2}]$

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Solution

Q. The potential energy of a particle changes with distance x from a fixed origin as V=Axx+B, where A and B are constant with appropriate dimensions. The dimension of AB are ______. [2026]

1 [M1L5/2T-2]

2 [M3/2L5/2T-2]

3 [M1L2T-2]

4 [M1L7/2T-2]

Ans. (4) [B]=[x]=[L] [A]=[PE]×[length]length=ML2T-2×LL1/2 [A]=[ML5/2T-2] [A·B]=[ML5/2T-2]×[L]=[ML7/2T-2]