Question

Consider the equation $\frac{d}{d t}\left[\displaystyle \int \overset{ \rightarrow }{F} \cdot d \overset{ \rightarrow }{s}\right]=A\left[\right.\overset{ \rightarrow }{F}\cdot \overset{ \rightarrow }{P}\left]\right..$ Then dimensions of $A$ will be $\left(\right.$ where $\overset{ \rightarrow }{F}=$ force $d\overset{ \rightarrow }{s}=$ small displacement, $t=$ time and $\overset{ \rightarrow }{P}=$ linear momentum $\left.$

• A. $\left[M^{0} L^{0} T^{0}\right]$
• B. $\left[M^{1} L^{0} T^{0}\right]$
• C. $\left[M^{- 1} L^{0} T^{0}\right]$
• D. $\left[M^{0} L^{0} T^{- 1}\right]$

Answer 1

Answer: (C)

$A=\frac{\frac{d}{d t} \left[\displaystyle \int \overset{ \rightarrow }{F} \cdot d \overset{ \rightarrow }{s}\right]}{\left[\overset{ \rightarrow }{F} \cdot \overset{ \rightarrow }{p}\right]}$
$=\frac{\left[\right. \text{ work } \left]\right.}{\text{ time } \times \frac{\text{ work }}{\text{ displacement }} \times P}=\frac{1}{M}$