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 =10^(3) g`
`1 kg m^2 s^(–2) = 1 kg × 1 m^2 × 1 s^(–2)`
`=10^3 g × 10^4 cm^2 × 1 s^(–2) = 10^7 g cm^2 s^(–2)`
(b) light year is the total distance travelled by light in one year
1 y =speed of ligtht ×one year
`= (3 × 10^8 m/s) × (365 × 24 × 60 × 60 s)`
`= 9.46 × 10^(15) m`
`:.1m =1/(9.46xx10^(15)) 1.057xx10^(-16) ly`
(c) `1m=10^(–3) km`
Again `1s=1/3600 h`
`1 s^(–1) = 3600 h^(–1)`
`1 s^(–2) = (3600)^2 h^(–2)`
`∴3 m s^(–2) = (3 × 10'^(–3) km) × ((3600)^2 h^(–2)) = 3.88 × 10^4 km h^(–2)`
(d) `1N=1kg ms^(–2)`
`1 kg = 10^(–3) g^(–1)`
`1m^(3) =10^(6) cm^(3)`
`∴ 6.67 × 10^(–11) N m^2 kg^(–2) = 6.67 × 10^(–11) × (1 kg m s^(–2)) (1 m^2) (1 s^(–2))`
`= 6.67 × 10^(–11) × (1 kg × 1 m^3 × 1 s^(–2))
= 6.67 × 10^(–11) × (10^(–3) g^(–1)) × (10^6 cm^3) × (1 s^(–2)) = 6.67 × 10^(–8) cm^3 s^(–2) g^(–1)`