Fill in the blanks by suitable conversion of units: (a) 1 kg m2s–2= ....g cm2 s–2 (b) 1 m =..... ly (c) 3.0 m s–2=.... km h–2 (d) G= 6.67 × 10–11 N m2 (kg)–2=.... (cm)3s–2 g–1.

Fill in the blanks by suitable conversion of units:
(a) 1 kg m2s–2= ....g cm2 s–2
(b) 1 m =..... ly
(c) 3.0 m s–2=.... km h–2
(d) G= 6.67 × 10–11 N m2 (kg)–2=.... (cm)3s–2 g–1.
Answer:
(a) 1 kg = 103 g
1 m2 = 104 cm2
1 kg m2 s–2 = 1 kg × 1 m2 × 1 s–2
=10^3 g × 10^4 cm2 × 1 s–2 = 10^7 g cm2 s–2
(b) Light year is the total distance travelled by light in one year.
1 ly = Speed of light × One year
= (3 × 108 m/s) × (365 × 24 × 60 × 60 s)
= 9.46 × 10^15 m

(c) 1 m = 10–3 km
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) 1 N = 1 kg m s–2
1 kg = 10–3 g–1
1 m3 = 106 cm3
∴ 6.67 × 10^–11 N m2 kg–2 = 6.67 × 10^–11 × (1 kg m s–2) (1 m2) (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 cm3) × (1 s–2)
= 6.67 × 10^–8 cm^3 s^–2 g^–1