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JEE Main201911 Jan 2019Morning ShiftPhysicsUnits and DimensionsActual

The force of interaction between two atoms is given by F= (- x² k T ) ; where x is the distance, k is the Boltzmann constant and T is temperature and and are two constants. The dimensions of is:

Options

  1. AM ⁰ ~L ² ~T ⁻⁴
  2. BM ² LT ⁻⁴
  3. CMLT ⁻²
  4. DM ² ~L ² ~T ⁻²

Correct answer

B. M ² LT ⁻⁴

Step-by-step solution

Force of interaction between two atoms, F = e ^ ( - x ² kT ) Since exponential terms are dimensionless [ x ² k T ]= M ⁰ ~L ⁰ ~T ⁰ L ² [ ] ML ² ~T ⁻² = M ⁰ ~L ⁰ ~T ⁰ [ ]= M ⁻¹ ~T ²[ F ]=[ ][ ] MLT ⁻²= M ⁻¹ ~T ²[ ] [ ]=M² L T⁻⁴

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