Fill in the blanks by suitable conversion of units :
(a) `1kg m^2 s^(-2) = g cm^2 s^(-2)` (b) 1m = ……. Light year (c ) `3ms^(-2) = ….. Km h^(-2)`
(d) `G = 6.67 xx10^(-11) Nm^2 kg^(-2) = …… cm^3 s^(-2) g^(-1)`

Explanation

(a) `1kg m^2 s^(-2) = 1 xx10^3 g (10^2 cm)^2 = s^(-2) = 10^7 g cm^23 s^(-2)`
(b) We know, 1 light year `= 9.46xx10^(15)m :. 1m = (1)/(9.46xx10^(15)) light year = 1.053xx10^(-16) light year`
(c ) `3ms^(-2) = 3xx10^(-3) km ((1)/(60xx60)h)^2 = 3xx10^(-3) xx3600xx3600km h^(-2) = 3.888xx10^4 km h^(-2)`
(d) `G = 6.67xx10^(-11)(kg ms^(-2))m^2 kg^(-2)`
`= 6.67xx10^(11)m^3 s^(-2) kg^(-1) = 6x67xx10^(-11) (100cm)^3 s^(-2) (1000g)^(-1) = 6.67xx10^(-8) cm^3 s^(-2) g^(-1)`