Question

Fill in the blanks by suitable conversion of units:

1 kg m²s^-2 = ...................g cm²s^-2

1 m =.................. ly

3.0 m s^–2 =.... km h^–2 

G= 6.67 × 10^–11 N m² (kg)^–2 =.... (cm)³s^–2 g^–1.

Answer 1

1 kg = 10³ g

1 m² = 10⁴ cm².

1 kg m² s^–2 = 1 kg × 1 m² × 1 s^–2.

=10³ g × 10⁴ cm² × 1 s^–2 = 10⁷ g cm² s^–2.

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 x 10¹⁵m

1 m = (1/9.46 x 10¹⁵) = 1.057 x 10^-16 ly

1 m = 10^-3 km

Again, 1 s = (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

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 m³ × 1 s^–2)

= 6.67 × 10^–11 × (10^–3 g^–1) × (10⁶ cm³) × (1 s^–2)

= 6.67 × 10^–8 cm3 s^–2 g^–1