Question

In the equation x=Asin(bt) dimensional formula for b is: (spam answers will be reported)​

Answer 1

Given:

$\boxed{ \bf{x = A \sin(bt) }}$

To find:

Dimensional formula of "b" ?

Calculation:

In tis type of questions (involving trigonometric function), we need to apply the following rule :

Quantities inside a trigonometric function are dimension-less.

This is because quantities in a trigonometric function represent "angles" , which are dimension-less.

So , we can say that (b × t) is dimension-less.

$\therefore \: \rm \bigg \{bt \bigg \} = \bigg \{{M}^{0} {L}^{0} {T}^{0} \bigg \}$

$\implies \: \rm \bigg \{b \times T \bigg \} = \bigg \{{M}^{0} {L}^{0} {T}^{0} \bigg \}$

$\implies \: \rm \bigg \{b\bigg \} = \bigg \{ \dfrac{{M}^{0} {L}^{0} {T}^{0}}{T} \bigg \}$

$\implies \: \rm \bigg \{b\bigg \} = \bigg \{{M}^{0} {L}^{0} {T}^{ - 1} \bigg \}$

So, dimensional formula of "b" is :

$\boxed{ \bf{ \bigg \{b\bigg \} = \bigg \{{M}^{0} {L}^{0} {T}^{ - 1} \bigg \}}}$