### Q.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}.

**Answer:-**

(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}

1 kg m^{2}s^{–2}= __10__^{7} g cm^{2} s^{–2}

(b) Distance = Speed × Time

Speed of light = 3 × 10^{8} m/s

Time = 1 year = 365 days = 365 × 24 hours = 365 × 24 × 60 × 60 sec

Putting these values in above formula we get

1 light year distance = (3 × 10^{8} m/s) × (365 × 24 × 60 × 60 s) = 9.46 × 10^{15} m

9.46 × 10^{15} m = 1 ly

So that 1 m = 1/ 9.46 × 10^{15} ly = __1.06 × 10__^{-16} ly

(c) 1 hour = 3600 sec so that 1 sec = 1/3600 hour

1 km = 1000 m so that 1 m = 1/1000 km

3.0 m s^{–2} = 3.0 (1/1000 km)( 1/3600 hour)^{-2} = 3.0 × 10^{–3} km × ((1/3600)^{-2} h–2)

= 3.0 × 10^{–3} km × (3600)^{2} h^{–2} = 3.88 × 10^{4} km h^{–2}

3.0 m s^{–2}= __3.88 × 10__^{4} km h^{–2}

^{
}(d) Given,

G= 6.67 × 10^{–11} N m^{2} (kg)^{–2}

We know that

1 N = 1 kg m s^{–}2

1 kg = 10^{3} g

1 m = 100 cm = 10^{2} cm

Putting above values, we get

6.67 × 10^{–11} N m^{2} kg^{–2} = 6.67 × 10^{–11} × (1 kg m s^{–2}) (1 m^{2}) (1Kg^{–2})

Solve and cancel out the units we get

⇒ 6.67 × 10^{–11} × (1 kg^{–1} × 1 m^{3} × 1 s^{–2})

Putting above values to convert Kg to g and m to cm

⇒ 6.67 × 10^{–11} × (10^{3} g)^{-1} × (10^{2} cm)^{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}

G= 6.67 × 10^{–11} N m^{2} (kg)^{–2}= __6.67 × 10__^{–8} (cm)^{3}s^{–2} g^{–1}.