Match List-I with List-II
List-I:
(a) Gravitational constant (G)
(b) Gravitational potential energy
(c) Gravitational potential
(d) Gravitational intensity
List-II:
(i) $[\mathrm{L^2T^{-2}}]$
(ii) $[\mathrm{M^{-1}L^3T^{-2}}]$
(iii) $[\mathrm{LT^{-2}}]$
(iv) $[\mathrm{ML^2T^{-2}}]$
Choose the correct answer from the options given below
Answer: (C) (a) - (ii), (b) - (iv), (c) - (i), (d) - (iii)
(a) From $F = \dfrac{Gm_1m_2}{r^2}$: $[G] = \dfrac{[\mathrm{MLT^{-2}}][\mathrm{L^2}]}{[\mathrm{M^2}]} = [\mathrm{M^{-1}L^3T^{-2}}]$ (ii).
(b) Potential energy is an energy: $[\mathrm{ML^2T^{-2}}]$ (iv).
(c) Potential = energy per unit mass: $[\mathrm{L^2T^{-2}}]$ (i).
(d) Intensity = force per unit mass, an acceleration: $[\mathrm{LT^{-2}}]$ (iii).
Solution by Sreeraj P, M.Sc Physics