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JEE Main202312 Apr 2023Morning ShiftPhysicsUnits and DimensionsActual

Match List I with List II List-I List-II A Spring constant I [ T – 1 ] B Angular speed II [ M T – 2 ] C Angular momentum III [ M L 2 ] D Moment of Inertia IV [ M L 2 T – 1 ] Choose the correct answer from the options given below:

Options

  1. AA-I, B-III, C-II, D-IV
  2. BA-IV, B-I, C-III, D-II
  3. CA-II, B-I, C-IV, D-III
  4. DA-II, B-III, C-I, D-IV

Correct answer

C. A-II, B-I, C-IV, D-III

Step-by-step solution

The formula to calculate the spring constant is F = k x       . . . 1 The formula to calculate the angular speed is ω = 2 π T       . . . 2 The formula to calculate the angular momentum is L = m v r       . . . ( 3 ) The formula to calculate the moment of inertia is I = M R 2       . . . 4 Use the method of dimensional analysis to obtain the dimensions of the required quantities. From above relations, we can write M L T - 2 = k L ⇒ k = M T

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