First slide

Dimensions of physical quantities

Question

Consider the expression $\int \frac{v \times d v}{g - b v^{2}} = a$ , in which v and g are speed and acceleration due to gravity respectively. What is the dimensional formula of ‘a’.

Moderate

A

$L^{- 1}$
B

$T^{- 2}$
C

$L$
D

$T^{- 1} L^{- 2}$

Solution

Given Expression $\int \frac{v d v}{g - b v^{2}} = a$
Where v=Speed= $L T^{- 1}$
g= acceleration due to gravity= $L T^{- 2}$
According to principle of homogenity g-b $v^{2}$ will have the dimensions of acceleration due to gravity.
Dimensionally
$\begin{array}{l} [a] = \frac{[V^{2}]}{[g]} \\ = \frac{{(L T^{- 1})}^{2}}{L T^{- 2}} = L \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App