Question

Prove with the help of dimensional analysis that the
equation h=1/2gt for the distance travelled by a body falling freely under gravity in time t is incorrect. Find the correct equation with the help of dimensions​

Answer 1

To check:

Equation h = ½gt is incorrect with the help of dimensional analysis.

Solution:

We need to separately check the LHS and RHS of the equation using dimensional analysis.

In dimensional analysis, we will express each and every quantity in terms of basic physical quantities like mass, length and time.

LHS:

$\therefore \bigg \{h \bigg \} = \bigg \{L \bigg \}$

RHS:

$\therefore \bigg \{ \dfrac{1}{2} gt\bigg \} = \bigg \{acceleration \times time\bigg \}$

$= > \bigg \{ \dfrac{1}{2} gt\bigg \} = \bigg \{ L{T}^{ - 2} \bigg \} \times \bigg \{ T\bigg \}$

$= > \bigg \{ \dfrac{1}{2} gt\bigg \} = \bigg \{ L{T}^{ - 1} \bigg \}$

Hence , we can say that :

$\boxed{ \bold{ \red{RHS \: \neq \: LHS}}}$

So, the Equation is incorrect.

Answer 2

Explanation:

answer for the question