# Q 2.2: Fill in the blanks by suitable conversion of units(a) $1 kg m^2s^-^2 = \ \ \ \ \ \ \ \ gcm^2s^-^2$b) $1 m = \ \ \ \ ly$(c) $3.0 \ m s^-^2 = \ \ \ \ km h^-^2$(d)$G = 6.67 \times 10^{-11} Nm^2(kg)^-^2 = \ \ \ \ \ (cm)^3 s^{-2}g^{-1}$.

(a) $(1 kg \rightarrow 1000g ;\ 1m\rightarrow 100 cm)$

$1 kgm^2s^{-2} = (1000g)(100cm)^2s^{-2} = (10^3 \times10^{4})gcm^2s^{-2} = 10^{7}\ gcm^2s^{-2}$

(b) $1 m = 1.057\times10^{-16} ly$   (1 ly = Distance travelled by light in 1 year )

(c) $(1 m \rightarrow 10^{-3}km ;\ (60\times60 =) 3600 s \rightarrow 1hr)$

$\\3.0 ms^{-2} = 3.0 (10^{-3}km)(1/3600 hr)^{-2} = 3.0 \times (3600)^2 / 1000\ kmhr^{-2} \\ = 3.9 \times 10^4 \ kmhr^{-2}$

(d)    $(N \rightarrow J.s = kgms^{-2};\ 1 m \rightarrow 100cm;\ 1 kg\rightarrow 1000g)$

$G = 6.67 \times 10^{-11} (kgms^{-2})m^2kg^-^2 = (6.67 \times 10^{-11})(m)^3 s^{-2}kg^{-1} = 6.67 \times 10^{-8}cm^3 s^{-2}g^{-1}$

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