The potential energy of a… - JEE Main 2026 Physics PYQ

JEE Main 2026 — Physics Mechanics

2026mcqmedium

The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \dfrac{A\sqrt{x}}{x + B}$ , where $A$ and $B$ are constant with appropriate dimensions. The dimensions of $AB$ are _______.

Official previous-year question

Held on 6 Apr 2026 · Verified 6 Jul 2026.

Options

A
$[M^1 L^{5/2} T^{-2}]$
B
$[M^{3/2} L^{5/2} T^{-2}]$
C
$[M^1 L^2 T^{-2}]$
D
$[M^1 L^{7/2} T^{-2}]$

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Solution

By the principle of dimensional homogeneity, quantities added or subtracted must have the same dimensions. In the denominator, $B$ is added to $x$ (distance).

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

The dimensions of potential energy $V$ are $[M^1 L^2 T^{-2}]$ .

From the given equation $V = \dfrac{A\sqrt{x}}{x + B}$ , we can write the dimensional formula as:

$[V] = \dfrac{[A][x]^{1/2}}{[x + B]}$

$[M^1 L^2 T^{-2}] = \dfrac{[A][L]^{1/2}}{[L]}$

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

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

Now, the dimensions of $AB$ are:

$[AB] = [A][B] = [M^1 L^{5/2} T^{-2}][L] = [M^1 L^{7/2} T^{-2}]$

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

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Solution

By the principle of dimensional homogeneity, quantities added or subtracted must have the same dimensions. In the denominator, $B$ is added to $x$ (distance).

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

The dimensions of potential energy $V$ are $[M^1 L^2 T^{-2}]$ .

From the given equation $V = \dfrac{A\sqrt{x}}{x + B}$ , we can write the dimensional formula as:

$[V] = \dfrac{[A][x]^{1/2}}{[x + B]}$

$[M^1 L^2 T^{-2}] = \dfrac{[A][L]^{1/2}}{[L]}$

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

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

Now, the dimensions of $AB$ are:

$[AB] = [A][B] = [M^1 L^{5/2} T^{-2}][L] = [M^1 L^{7/2} T^{-2}]$

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

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Options

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics