Fill in the blanks by suitable conversion of units

(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:

(c) We know that 1 km = 1000m

So, 1m = 1/1000 km

Then, 3.0 m s^-2 = 3.0 (1/1000 km) (1/3600 hour) ^-2 

= 3.0 x 10^-3 km x ((1/3600)^-2h^-2)

= 3 x 10^-3km x (3600)² hr^-2 

Therefore, 3.0 m s^-2 = 3.88 x 10⁴ km h­^-2

(d) we have => G = 6.67 x 10^-11 N m² (kg)^-2

We know that 1N = 1kg m s^-2

Where1 kg = 10³ g and 1m = 100cm= 10² cm

Putting these values in G, we have :

=> 6.67 x 10^-11 Nm² kg^-2 

= 6.67 x 10^-11 x (1kg m s ^-2) (1m²) (1kg^-2)

=> 6.67 x 10^-11 x (1kg ^-1 x 1m³ x 1s^-2)

Converting kg to g and m to cm, we get –

= 6.67 x 10^-11 x (10³g)^-1 x (10² cm)³ x (1s^-2) = 6.67 x 10^-8 cm³ s^-2 g ^-1

Therefore, G = 6.67 x 10^-8  (cm)³ s^-2 g ^-1