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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Introduction to Physics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Introduction to Physics

Assume a quantity x can be dimensionally expressed in terms of M ,...

Assume a quantity

x

can be dimensionally expressed in terms of

M

,

L

, and

T

, such that

[x] = M^a L^b T^c

. The quantity mass

Options

Amay be expressed in terms of $L$ , $T$ , and $x$ if $a \neq 0$
Bcan never be dimensionally expressed in terms of $L$ , $T$ , and $x$
Ccan always be dimensionally expressed in terms of $L$ , $T$ , and $x$
Dmay be expressed in terms of $L$ , $T$ , and $x$ if $a = 0$

Correct answer

A. may be expressed in terms of $L$ , $T$ , and $x$ if $a \neq 0$

Step-by-step solution

Given

[x] = M^a L^b T^c

Rearranging the terms to express

M

in terms of

x

,

L

, and

T

:

M^a = [x] L^{-b} T^{-c}

M = [x]^{1/a} L^{-b/a} T^{-c/a}

For this relation to be valid, the exponent

1/a

must be defined, which requires

a \neq 0

.

Therefore, mass may be expressed in terms of

L

,

T

, and

x

if

a \neq 0

.

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