Question

4. Check the validity of given expression: (i)y = a +vt where y is position at any time t of any particle
having speed v and a is amplitude. ​

Answer 1

Given:

$y = a + vt$

To check:

Validity of the equation ?

Calculation:

• We will use DIMENSIONAL ANALYSIS to solve this type of questions !

LHS :

$\bigg \{y \bigg \} = \bigg \{{M}^{0} L{T}^{0} \bigg \}$

Now, RHS:

$\bigg \{a + vt \bigg \} = \bigg \{length + length \bigg \}$

$\implies \bigg \{a + vt \bigg \} = \bigg \{ L\bigg \}$

$\implies\bigg \{a + vt \bigg \} = \bigg \{{M}^{0} L{T}^{0} \bigg \}$

So, LHS = RHS, hence equation is dimensionally valid .