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Chapter 1: Problem 15

Which of the following group have different dimension? (A) Potential difference, EMF, voltage (B) Pressure, stress, Young's modulus (C) Heat, energy, work-done (D) Dipole moment, electric-flux, electric field

Short Answer

Expert verified
The group with different dimensions is (D) Dipole moment, Electric-flux, and Electric field. The dimensions of Dipole moment are \([M^0 L^2 I T^-1]\), Electric-flux are \([M^0 L^3 I T^-3]\), and Electric field are \([M L T^-3 I^-1]\).

Step by step solution

01

Familiarity with the Dimensions of the Given Quantities.

The first step is to be familiar with the dimensions of the given quantities in each group. Here are the dimensions of the quantities in each group: (A) Potential difference, EMF, Voltage: Dimensions of all three quantities are [M L^2 T^-3 I^-1] (B) Pressure, Stress, Young's modulus: Dimensions of Pressure and Stress are [M L^-1 T^-2], and the dimensions of the Young's modulus are [M L^-1 T^-2] (C) Heat, Energy, Work-done: Dimensions of all three quantities are [M L^2 T^-2] (D) Dipole moment, Electric-flux, Electric field: Dimensions of Dipole moment are [M^0 L^2 I T^-1], Electric-flux are [M^0 L^3 I T^-3], and the dimensions of the Electric field are [M L T^-3 I^-1]
02

Comparing The Dimensions of the Quantities in Each Group

After knowing the dimensions of each quantity we can now identify which group has quantities with different dimensions. Upon comparison, we found out that in groups (A), (B), (C), all the three quantities have the same dimensions, while in group (D) the quantities have different dimensions. Therefore, the group (D) which contains Dipole moment, Electric-flux, and Electric field, has different dimensions and is the answer to the given exercise.

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Most popular questions from this chapter

The dimensions of magnetic field in \(M, L, T\) and \(C\) (Coulomb) is given as (A) \(\left[M L T^{-1} C^{-1}\right]\) (B) \(\left[M T^{2} C^{-2}\right]\) (C) \(\left[M T^{-1} C^{-1}\right]\) (D) \(\left[M T^{-2} C^{-1}\right]\)

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