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Question

The root mean square velocity of a gas is given by

This question was previously asked in
CUET PG 2026 Agri-Business Management Question Paper (25-Mar-2026) (Shift 2)
The correct answer is
$\sqrt{\frac{3RT}{M}}$

Gas RMS Velocity Formula

The root mean square (RMS) velocity ($v_{rms}$) is a measure of the speed of particles in a gas, derived from the kinetic theory of gases.

Standard Formula

The mathematical expression for the RMS velocity of an ideal gas is:

$v_{rms} = \sqrt{\frac{3RT}{M}}$

  • Where:
    • $v_{rms}$ denotes the root mean square velocity.
    • $R$ represents the ideal gas constant.
    • $T$ is the absolute temperature in Kelvin.
    • $M$ is the molar mass of the gas (in appropriate units, typically kg/mol).

Identifying the Correct Option

By comparing the standard formula $v_{rms} = \sqrt{\frac{3RT}{M}}$ with the choices provided, the correct option is identified.

$\sqrt{\frac{3RT}{M}}$

This corresponds to Option 1.

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