The value of the universal gravitational constant is 6 . 67 × 10 - 11 N m 2 kg - 2 . Find its value in g - 1 cm 3 s - 2 .

As we know that : 1 N = 1 kg × ms - 2 So, 1 Nm 2 kg - 2 = 1 kg ms - 2 × m 2 kg 2 = 1 kg - 1 m 3 s - 2 And 1 kg = 10 3 g , 1 m = 10 2 cm therefore, 1 kg - 1 m 3 s - 2 = ( 10 3 g ) - 1 × ( 10 2 c m ) 3 s - 2 = 10 - 3 g - 1 × 10 6 cm 3 s - 2 Hence 1 kg - 1 m 3 s - 2 = 10 3 g - 1 cm 3 s - 2 The value of G = 6 . 6 × 10 - 11 × 10 3 g - 1 cm 3 s - 2 = 6 . 67 × 10 - 8 gm - 1 cm 3 s - 2

The value of Stefan's constant is σ = 5 . 67 × 10 - 5 ergs - 1 cm - 2 K - 4 . Find its value in SI units.

As we know that: 1 erg = 10 - 7 J and 1 m = 100 cm Therefore, substituting these values, we have the stephan's constant in S I units: σ = 5 . 67 × 10 - 5 ergs - 1 cm - 2 K - 4 = 5 . 67 × 10 - 5 × 10 - 7 Js - 1 ( 10 - 2 m ) - 2 K - 4 σ = 5 . 67 × 10 - 8 J s - 1 m - 2 K - 4

Express speed of light ( 3 . 0 × 10 8 m / s ) in terms of AU per min.

Astronomical unit A U is used to measure large distances in space. Following are the conversion factors for the various units 1 km = 1000 m 1 AU = 1 . 5 × 10 8 km 1 min = 60 s Thus, using the above relations the speed of light c = 3 × 10 8 meter / s can be written as: c = 3 × 10 8 m s = 3 × 10 8 1000 kms - 1 = 3 × 10 8 1000 × 1 . 5 × 10 8 60 1 = 0 . 12 AU / min