Fill in the blanks by suitable conversion of units (a) 1 kg m2 s-2 = �. g cm2 s-2 (b) 1 m =���� ly (c) 3.0 m s-2 = �. km h-2 (d) G = 6.67 x 10-11 N m2 (kg)-2 = �. (cm)3 s-2 g-1

(a) 1 kg = 103g1 m2= 104cm21 kg m2s–2= 1 kg × 1 m2× 1 s–2=103g × 104cm2× 1 s–2= 107g cm2s–21 kg m2s–2=107g cm2s–2 (b)Distance = Speed × TimeSpeed of light = 3 × 108m/sTime = 1 year = 365 days = 365 × 24 hours = 365 × 24 × 60 × 60 secPutting these values in above formula we get1 light year distance = (3 × 108m/s) × (365 × 24 × 60 × 60 s) = 9.46 × 1015m9.46 × 1015m = 1 lySo that 1 m = 1/ 9.46 × 1015ly =1.06 × 10–16ly (c) 1 hour = 3600 sec so that 1 sec = 1/3600 hour1 km = 1000 m so that 1 m = 1/1000 km3.0 m s–2= 3.0 (1/1000 km)( 1/3600 hour)-2= 3.0 × 10–3km × ((1/3600)-2h–2)= 3.0 × 10–3km × (3600)2h–2= 3.88 × 104km h–23.0 m s–2=3.88 × 104km h–2(d)Given,G= 6.67 × 10–11N m2kg–2We know that1 N = 1 kg m s–21 kg = 103g1 m = 100 cm = 102cmPutting above values, we get6.67 × 10–11N m2kg–2= 6.67 × 10–11× (1 kg m s–2) (1 m2) (1Kg–2)Solve and cancel out the units, we get⇒ 6.67 × 10–11× (1 kg–1× 1 m3× 1 s–2)Putting above values to convert kg to g and m to cm⇒ 6.67 × 10–11× (103g)-1× (102cm)3× (1 s–2)⇒ 6.67 × 10–11× 10-3g-1× 106cm3× (1 s–2)⇒ 6.67 × 10–8cm3s–2g–1G= 6.67 × 10–11N m2kg–2 =6.67 × 10–8cm3s–2g–1 read less