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Units and Measurements question

2023 · 31 Jan · Shift 2 · Q58
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Units and Measurements question

2023 · 31 Jan · Shift 2 · Q58

JEE MainPhysicsUnits and MeasurementsMCQ+4 / −1
Match List I with List II

LIST I LIST II
A. Angular momentum I. [ML2 T−2]\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right][ML2 T−2]
B. Torque II. [ML−2 T−2]\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right][ML−2 T−2]
C. Stress III [ML2 T−1]\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right][ML2 T−1]
D. Pressure gradient IV. [ML−1 T−2]\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right][ML−1 T−2]

Choose the correct answer from the options given below:
  1. A
    A - I, B - IV, C - III, D - II
  2. B
    A - III, B - I, C - IV, D - II
  3. C
    A - IV, B - II, C - I, D - III
  4. D
    A - II, B - III, C - IV, D - I
View written solutionFree

Correct answer: B

  1. Find dimensions of each quantity in List I

A. Angular momentum

Angular momentum LLL is L=r×pL = r \times pL=r×p where momentum p=mvp = mvp=mv.

So, [L]=[M][L][LT−1]=[ML2T−1][L] = [M][L]\left[LT^{-1}\right] = \left[ML^2T^{-1}\right][L]=[M][L][LT−1]=[ML2T−1] Thus, A→IIIA \to \text{III}A→III

B. Torque

Torque is τ=r×F\tau = r \times Fτ=r×F Now, [F]=[MLT−2][F] = [MLT^{-2}][F]=[MLT−2] Hence, [τ]=[L][MLT−2]=[ML2T−2][\tau] = [L][MLT^{-2}] = \left[ML^2T^{-2}\right][τ]=[L][MLT−2]=[ML2T−2] Thus, B→IB \to \text{I}B→I

C. Stress

Stress is force per unit area: Stress=FA\text{Stress} = \frac{F}{A}Stress=AF​ So, [Stress]=[MLT−2][L2]=[ML−1T−2][\text{Stress}] = \frac{[MLT^{-2}]}{[L^2]} = \left[ML^{-1}T^{-2}\right][Stress]=[L2][MLT−2]​=[ML−1T−2] Thus, C→IVC \to \text{IV}C→IV

D. Pressure gradient

Pressure gradient is pressure per unit length.

Pressure has dimensions: [P]=[F][A]=[MLT−2][L2]=[ML−1T−2][P] = \frac{[F]}{[A]} = \frac{[MLT^{-2}]}{[L^2]} = \left[ML^{-1}T^{-2}\right][P]=[A][F]​=[L2][MLT−2]​=[ML−1T−2] Therefore, [Pressure gradient]=[P][L]=[ML−2T−2][\text{Pressure gradient}] = \frac{[P]}{[L]} = \left[ML^{-2}T^{-2}\right][Pressure gradient]=[L][P]​=[ML−2T−2] Thus, D→IID \to \text{II}D→II

  1. Final matching

A→III,B→I,C→IV,D→IIA \to \text{III}, \quad B \to \text{I}, \quad C \to \text{IV}, \quad D \to \text{II}A→III,B→I,C→IV,D→II

This corresponds to Option B.

  1. Comparison with stored answer

Stored correct answer: B

My derived answer: B

So, the answer agrees with the stored correct answer.

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