Question

Consider the equation $\frac{ d }{ dt }\left(\int \overrightarrow{ F } \cdot d \overrightarrow{ S }\right)= A (\overrightarrow{ F } \cdot \overrightarrow{ p })$ where $\overrightarrow{ F }=$ force, $\overrightarrow{ s }=$ displacement, $t =$ time and $\overrightarrow{ p }=$ momentum. The dimensional formula of $A$ will be

• A. $M ^{0} L ^{0} T ^{0}$
• B. $ML^{0} T ^{0}$
• C. $M^{-1} L^{0} T^{0}$
• D. $M^{0} L^{0} T^{-1}$

Answer 1

Answer: (C)

$\left[\frac{ d }{ dt }\left(\int \overrightarrow{ F } \cdot d \overrightarrow{ S }\right)\right]$
$=[ A (\overrightarrow{ F } \cdot \overrightarrow{ p })]$
$\Rightarrow \left[\frac{ Fs }{ t }\right]=[ AFp ]$
$\Rightarrow [ A ]=\left[\frac{ s }{ pt }\right]$
$=\frac{ L }{ MLT ^{-1} \times T }= M ^{-1}$