Question

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 1

(a) 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

(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 × 10¹⁵ m

(c) 1 m = 10^–3 km

Again, 1 s =

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 × 10⁴ 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 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