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) `1kgm^(2)s^(-2)= 1(10^(3)g)(10^(2)cm)^(2)s^(-2)`
`=10^(7)gcm^(2)s^(-2)`.
(b) As 1 light year `=9.46xx10^(15)m`, therefore,
`1m= 1"/"9.46xx10^(15)=1.057xx10^(-16)` light year
`approx 10^(-16)` light year.
(c ) `3ms^(-2)=3((1)/(1000)km)((1)/((60xx60))hr)^(-2)`
`=3.888xx10^(4) kmh^(-2)`
`=3.9xx10^(4) kmh^(-2)`.
(d) `G= 6.67xx10^(-11)Nm^(2)(kg)^(-2)`
`G=6.67xx10^(-11)(10^(5)"dyne")(100cm)^(2)(1000g)^(-2)`
`=6.67xx10^(-8)"dyne"cm^(2)g^(-2)`
`=6.67xx10^(-8)gcms^(-2)cm^(2)g^(-2)`
`=6.67xx10^(-8)cm^(3)s^(-2)g^(-1)`.