1.Units, Dimensions and Measurement
medium

मात्रकों की किसी पद्धति में यदि बल $(F)$, त्वरण $(a)$ एवं समय $(T) $ को मूल मात्रक माना जाये तो ऊर्जा का विमीय-सूत्र होगा

A

$F{A^2}T$

B

$FA{T^2}$

C

${F^2}AT$

D

$FAT$

Solution

(b) $E = K{F^a}{A^b}{T^c}$

$[M{L^2}{T^{ – 2}}] = {[ML{T^{ – 2}}]^a}\,{[L{T^{ – 2}}]^b}\,{[T]^c}$

$[M{L^2}{T^{ – 2}}] = [{M^a}{L^{a + b}}{T^{ – 2a – 2b + c}}]$

$\therefore $ $a = 1$, $a + b = 2$ $⇒$ $b = 1$

तथा $ – 2a – 2b + c = – 2\;\; \Rightarrow \;c = 2$

$⇒$ $E = KFA{T^2}$

Standard 11
Physics

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