Consider the equation ( d / dt )(∫ F ⋅ d S )= A ( F ⋅ p ) where F = force, s = displacement, t = time and p = momentum. The dimensional formula of A will be

Question

Consider the equation ( d / dt )(∫ F ⋅ d S )= A ( F ⋅ p ) where F = force, s = displacement, t = time and p = momentum. The dimensional formula of A will be (A) M 0 L 0 T 0 (B) ML0 T 0 (C) M-1 L0 T0 (D) M0 L0 T-1

Tardigrade Admin · Accepted Answer

[( d / dt )(∫ F ⋅ d S )] =[ A ( F ⋅ p )] ⇒ [( Fs / t )]=[ AFp ] ⇒ [ A ]=[( s / pt )] =( L / MLT -1 × T )= M -1

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

$M^{0} L^{0} T^{0}$

$M L^{0} T^{0}$

$M^{- 1} L^{0} T^{0}$

$M^{0} L^{0} T^{- 1}$

$[\frac{d}{d t} (\int F \cdot d S)]$
$= [A (F \cdot p)]$
$\Rightarrow [\frac{F s}{t}] = [A Fp]$
$\Rightarrow [A] = [\frac{s}{pt}]$
$= \frac{L}{M L T ^{- 1} \times T} = M^{- 1}$

Q. Consider the equation dtd​(∫F⋅dS)=A(F⋅p​) where F= force, s= displacement, t= time and p​= momentum. The dimensional formula of A will be

M0L0T0

ML0T0

M−1L0T0

M0L0T−1