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Chapter 1: Problem 1

If we change unit of a physical quantity then (A) its dimension changes. (B) its dimension remain same. (C) it may change or may not change. (D) its magnitude changes.

Short Answer

Expert verified
The correct answer is (D) its magnitude changes, and the dimension remains the same (B). Changing the unit of a physical quantity does not change its dimensions, which are inherent properties describing its basic nature in terms of fundamental quantities. However, the magnitude usually changes depending on the unit system.

Step by step solution

01

Understanding Dimensions and Magnitude

Dimensions represent the basic nature of a physical quantity in terms of fundamental quantities like mass, length, and time. For example, the dimension of speed is [LT^(-1)], where L represents length and T represents time. The magnitude of a physical quantity is its numerical value in a specific unit system.
02

Effect of Changing Unit on Dimensions

When we change the unit of a physical quantity, its dimensions remain the same because dimensions are independent of the unit system. They are an inherent property of the physical quantity describing its basic nature. So, options (A) and (C) are incorrect.
03

Effect of Changing Unit on Magnitude

When we change the unit of a physical quantity, its magnitude usually changes because the numerical value depends on the unit system. For example, if we have a length of 10 meters, it is equivalent to 1000 centimeters. So, option (D) is correct.
04

Final Answer

Based on our analysis, the correct answer is: (D) its magnitude changes, and the dimension remains the same (B).

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Most popular questions from this chapter

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are \(3 \%\) each, then error in the value of resistance of the wire is (A) \(6 \%\) (B) Zero (C) \(1 \%\) (D) \(3 \%\)

Two vectors \(\vec{A}\) and \(\vec{B}\) have magnitude 3 each. \(\vec{A} \times \vec{B}=-5 \hat{k}+2 \hat{i}\). Find angle between \(A\) and \(B\) (A) \(\cos ^{-1} \frac{\sqrt{29}}{9}\) (B) \(\tan ^{-1}\left(\frac{-5}{2}\right)\) (C) \(\sin ^{-1}\left(\frac{2}{5}\right)\) (D) \(\sin ^{-1}\left(\frac{\sqrt{29}}{9}\right)\)

If there is a positive error of \(50 \%\) in the measurement of velocity of a body, then the error in the measurement of kinetic energy is (A) \(25_{-} \%\) (B) \(50 \%\) (C) \(100 \%\) (D) \(125 \%\)

\(\vec{A}=3 \hat{i}+4 \hat{j}+2 \hat{k}, \vec{B}=6 \hat{i}-\hat{j}+3 \hat{k}\). Find a vector paral- lel to \(\vec{A}\) whose magnitude is equal to that of \(\vec{B}\). (A) \(\sqrt{\frac{46}{29}}(3 \hat{i}+4 \hat{j}+2 \hat{k})\) (B) \(\sqrt{\frac{46}{29}}(6 \hat{i}-\hat{j}+3 \hat{k})\) (C) \(\sqrt{\frac{29}{46}}(3 \hat{i}+4 \hat{j}+2 \hat{k})\) (D) None

\(\int \frac{d x}{\sqrt{a^{2}-x^{2}}}=\frac{1}{a} \sin ^{-1} \frac{a}{x}\) (A) is dimensionally correct. (B) dimensionally incorrect. (C) such mathematical relations cannot be tested. (D) cannot say.
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