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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.

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Solution

(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


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