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JIPMER 2008

Exam: JIPMER
Year: 2008
Subject: Physics
Chapter: Units and Dimensions

JIPMER 2008 · Physics · Units and Dimensions

Given that y=A [((2 π)/(λ)(c t-x))] , where y and x are measured in...

Given that

y=A \sin \left[\left(\frac{2 \pi}{\lambda}(c t-x)\right)\right]

, where

y

and

x

are measured in metre. Which of the following statements is true?

Options

AThe unit of $\lambda$ is same as that of $x$ and $A$
BThe unit of $\lambda$ is same as that of $x$ but not of $A$
CThe unit of $c$ is same as that of $\frac{2 \pi}{\lambda}$
DThe unit of $(c t-x)$ is same as that of $\frac{2 \pi}{\lambda}$

Correct answer

A. The unit of $\lambda$ is same as that of $x$ and $A$

Step-by-step solution

Here

\frac{2 \pi}{\lambda}(c t-x)

is dimensionless. Hence,

\frac{c t}{\lambda}

is also dimensionless and unit of

c t

is same as that of

x

. Therefore, unit of

\lambda

is same as that of

x

. Also unit of

y

is same as that of

A

, which is also the unit of

x

.

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