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Chapter 15: Problem 2210

The dimensional formula of energy density is (A) \(\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-2}\) (B) \(\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\) (C) \(\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-3}\) (D) \(\mathrm{M}^{\mathrm{l}} \mathrm{L}^{0} \mathrm{~T}^{-3}\)

Short Answer

Expert verified
The short answer based on the given step-by-step solution is: The dimensional formula of energy density is (B) \(\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\).

Step by step solution

01

Identifying the dimensional formula for energy and volume

Since energy is given in dimensions of \(\mathrm{M}^1\mathrm{L}^2\mathrm{T}^{-2}\), we want to divide this quantity with the dimensions for volume to obtain the correct dimensional formula for energy density. Volume has dimensions of \(\mathrm{L}^3\).
02

Dividing energy dimensions by volume dimensions

To obtain the dimensional formula for energy density, we need to divide the energy dimensions by the volume dimensions: \[\frac{\mathrm{M}^1\mathrm{L}^2\mathrm{T}^{-2}}{\mathrm{L}^3}\]
03

Simplifying the obtained dimensions

After dividing the dimensions, we can simplify the expression: \[ \mathrm{M}^1 \mathrm{L}^2\mathrm{T}^{-2} \cdot \mathrm{L}^{-3} = \mathrm{M}^1 \mathrm{L}^{-1} \mathrm{T}^{-2} \]
04

Comparing the obtained dimensions with given options

Now we will compare our obtained dimensional formula with the given options to find the correct answer: (A) \(\mathrm{M}^1\mathrm{L}^0\mathrm{T}^{-2}\) (B) \(\mathrm{M}^1\mathrm{L}^{-1}\mathrm{T}^{-2}\) (C) \(\mathrm{M}^1\mathrm{L}^{-1}\mathrm{T}^{-3}\) (D) \(\mathrm{M}^1\mathrm{L}^0\mathrm{T}^{-3}\) Our obtained dimensional formula, \(\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\), matches with option (B). So, the correct answer is (B) \(\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}\).

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Most popular questions from this chapter

If the direction of magnetic field \(\mathrm{B}^{\rightarrow}\) at some instant is along + ve \(Z\) direction and the electromagnetic wave is propagating along + ve \(\mathrm{X}\) direction, then the direction of electric field \(\mathrm{E}^{\rightarrow}\) at that instant is (A) along - ve Y direction (B) along + ve Y direction (C) along + ve \(\mathrm{X}\) direction (B) along - ve \(\mathrm{X}\) direction

The dimensional formula of \(\mu_{0} \mathrm{E}_{0}\) is (A) \(L^{2} T^{-2}\) (B) \(L^{-2} T^{2}\) (C) \(\mathrm{L}^{1} \mathrm{~T}^{-1}\) (D) \({L}^{-1} \mathrm{~T}^{1}\)

In electromagnetic spectrum, the visible light lie between (A) radiowaves and microwaves (B) ultraviolet rays and infrared rays (C) ultraviolet rays and \(\mathrm{x}\) rays (D) infrared rays and microwaves

According to Maxwell, a changing electric field produces (A) emf (B) Electric current (C) magnetic field (D) radiation pressure

Which of the following have zero average value in a plane electromagnetic wave? (A) Electric energy (B) Magnetic energy (C) Electric field (D) None of these.
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