__Question 2.2__:

Fill in the blanks by suitable conversion of units

(a) 1 kg m

^{2}s–

^{-2}= ....g cm

^{2}s–

^{-2}

(b) 1 m = ..... ly

(c) 3.0 m s–

^{-2}= .... km h

^{-2}

(d) G = 6.67 × 10–11 N m

^{2}(kg)–

^{-2}= .... (cm)

^{3}s

^{-2}g

^{-1}.

__Solution__:

(a) 1 kg = 10

^{3}g

1 m

^{2}= 10

^{4}cm

^{2}

1 kg m

^{2}s

^{–2}= 1 kg × 1 m

^{2}× 1 s

^{–2}

=10

^{3}g × 10

^{4}cm

^{2 }× 1 s

^{–2}= 10

^{7}g cm

^{2}s

^{–2}

^{}(b) Light year is the total distance travelled by light in one year.

1 ly = Speed of light × One year

= (3 × 10

^{8}m/s) × (365 × 24 × 60 × 60 s)

= 9.46 × 10

^{15}m

∴ 1 m = 1

**/**(9.46 X 10

^{15}) = 1.057 X 10

^{-16}ly

(c) 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}

^{}(d) 1 N = 1 kg m s

^{–2}

1 kg = 10

^{–3}g

^{–1}

1 m

^{3}= 10

^{6}cm

^{3}

∴ 6.67 × 10

^{–11}N m

^{2}kg

^{–2}= 6.67 × 10

^{–11}× (1 kg m s

^{–2}) (1 m

^{2}) (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}cm

^{3}) × (1 s

^{–2})

= 6.67 × 10

^{–8}cm

^{3}s

^{–2}g

^{–1}

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