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Match List I with List II and select the...

Match List I with List II and select the correct answer using the codes given below the lists:
`{:(,"List I",,,"List II"),(P.,"Boltzmann constant",,1.,[ML^(2)T^(-1)]),(Q.,"Coefficient of viscosity",,2.,[ML^(-1)T^(-1)]),(R.,"Planck constant",,3.,[MLT^(-3)K^(-1)]),(S.,"Thermal conductivity",,4.,[ML^(2)T^(-2)K^(-1)]):}`

A

`P=3, Q=1, R=2, S=4`

B

`P=3, Q=2, R=1, S=4`

C

`P=4, Q=2, R=1, S=3`

D

`P=4, Q=1, R=2, S=3`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of matching List I with List II, we need to determine the dimensional formulas for each of the physical constants given in List I and then find the corresponding match in List II. ### Step-by-Step Solution: 1. **Identify the Boltzmann Constant (P)**: - The Boltzmann constant (k) relates energy at the particle level to temperature. Its dimensional formula is: \[ [k] = [ML^2T^{-2}K^{-1}] \] - **Match**: This corresponds to option 4 in List II. 2. **Identify the Coefficient of Viscosity (Q)**: - The coefficient of viscosity (η) measures a fluid's resistance to flow. Its dimensional formula is: \[ [η] = [ML^{-1}T^{-1}] \] - **Match**: This corresponds to option 2 in List II. 3. **Identify the Planck Constant (R)**: - The Planck constant (h) relates energy to frequency. Its dimensional formula is: \[ [h] = [ML^2T^{-1}] \] - **Match**: This corresponds to option 1 in List II. 4. **Identify the Thermal Conductivity (S)**: - Thermal conductivity (k) measures a material's ability to conduct heat. Its dimensional formula is: \[ [k] = [MLT^{-3}K^{-1}] \] - **Match**: This corresponds to option 3 in List II. ### Summary of Matches: - P (Boltzmann constant) → 4 - Q (Coefficient of viscosity) → 2 - R (Planck constant) → 1 - S (Thermal conductivity) → 3 ### Final Matching: Thus, the final matching is: - P → 4 - Q → 2 - R → 1 - S → 3 ### Answer: The correct code for the matches is **4 2 1 3**.

To solve the problem of matching List I with List II, we need to determine the dimensional formulas for each of the physical constants given in List I and then find the corresponding match in List II. ### Step-by-Step Solution: 1. **Identify the Boltzmann Constant (P)**: - The Boltzmann constant (k) relates energy at the particle level to temperature. Its dimensional formula is: \[ [k] = [ML^2T^{-2}K^{-1}] ...
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Match List I with List II and select the correct anwer using the codes given below

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