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 ‘b’.

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= $L T^{- 2}$
Dimensionally
$\begin{array}{l} [b] = \frac{[g]}{[v^{2}]} \\ = \frac{L T^{- 2}}{{(L T^{- 1})}^{2}} = L^{- 1} \end{array}$

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