Match List-I with List-II: (a) Gravitati | vedclass

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(A) $1$. Gravitational constant $(G)$: From $F = G \frac{m_1 m_2}{r^2}$,we have $G = \frac{F r^2}{m_1 m_2}$. Dimensional formula is $[MLT^{-2}][L^2] /

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$(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)$

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(A) $1$. Gravitational constant $(G)$: From $F = G \frac{m_1 m_2}{r^2}$,we have $G = \frac{F r^2}{m_1 m_2}$. Dimensional formula is $[MLT^{-2}][L^2] / [M^2] = [M^{-1}L^3T^{-2}]$. Thus,$(a)-(ii)$.$2$. Gravitational potential energy $(U)$: $U = -\frac{G M m}{r}$. Dimensional formula is $[MLT^{-2}][L] = [ML^2T^{-2}]$. Thus,$(b)-(iv)$.$3$. Gravitational potential $(V)$: $V = \frac{U}{m}$. Dimensional formula is $[ML^2T^{-2}] / [M] = [L^2T^{-2}]$. Thus,$(c)-(i)$.$4$. Gravitational intensity $(E)$: $E = \frac{F}{m}$. Dimensional formula is $[MLT^{-2}] / [M] = [LT^{-2}]$. Thus,$(d)-(iii)$.Therefore,the correct match is $(a)-(ii), (b)-(iv), (c)-(i), (d)-(iii)$.

$(a)$ Gravitational constant $(G)$	$(i)$ $[L^{2}T^{-2}]$
$(b)$ Gravitational potential energy	$(ii)$ $[M^{-1}L^{3}T^{-2}]$
$(c)$ Gravitational potential	$(iii)$ $[LT^{-2}]$
$(d)$ Gravitational intensity	$(iv)$ $[ML^{2}T^{-2}]$

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