Q.

Match List-I with List-II

 List-I List-II
(A)Angular Impulse (I)[M0 L2 T–2
(B)Latent Heat (II)[ML2 T–3 A–1
(C)Electrical resistivity(III)[ML2 T–1
(D)Electromotive force(IV)[ML3 T–3 A–2

Choose the correct answer from the options given below : 

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a

 (A)-(I), (B)-(III), (C)-(IV), (D)-(II) 

b

(A)-(III), (B)-(I), (C)-(II), (D)-(IV) 

c

(A)-(III), (B)-(I), (C)-(IV), (D)-(II)

d

 (A)-(II), (B)-(I), (C)-(IV), (D)-(III)

answer is A.

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Detailed Solution

Angular Impulse

  • Angular impulse = Torque × Time
  • Torque = Force × Distance = (MLT2)×L=ML2T2(MLT^{-2}) \times L = ML^2T^{-2}
  • Time = TT
  • Dimensional formula of Angular Impulse = ML2T1ML^2T^{-1}
  • (III) [ML²T⁻¹]

Latent Heat

  • Latent heat = Energy/Mass
  • Energy = Work = Force × Distance = (MLT2)×L=ML2T2(MLT^{-2}) \times L = ML^2T^{-2}
  • Mass = MM
  • Dimensional formula of Latent Heat = L2T2L^2T^{-2}
  • (I) [M⁰L²T⁻²]

Electrical Resistivity

  • Resistivity (ρ\rho) = Resistance × Length / Area
  • Resistance RR = V/IV/I
  • Using Ohm’s Law: V=IRV = IR
  • Voltage VV = Work/Charge = ML2T3A1ML^2T^{-3}A^{-1}
  • Current II = Charge/Time = AT1AT^{-1}
  • Resistance RR = V/I=ML2T3A2V/I = ML^2T^{-3}A^{-2}
  • Resistivity = R×LR \times L
  • Dimensional formula of Electrical Resistivity = ML3T3A2ML^3T^{-3}A^{-2}
  • (IV) [ML³T⁻³A⁻²]

Electromotive Force (EMF)

  • EMF is essentially voltage, and its dimensional formula is:
  • (II) [ML²T⁻³A⁻¹]

(A) → (III), (B) → (I), (C) → (IV), (D) → (II)

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