Question

Fill in the blanks by suitable conversion of units (a) 1 kg m² s¯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)3 s¯² g¯¹

Answer 1

(a)

The suitable unit conversion is,

1 kg⋅ m 2 ⋅ s −2 =1000 g× ( 10 2  cm ) 2 × 1 s 2 = 10 7  g⋅ cm 2 ⋅ s −2

Thus,

1 kg⋅ m 2 ⋅ s −2 = 10 7  g⋅ cm 2 ⋅ s −2 .

(b)

The suitable unit conversion is,

1 m=1× 10 −16  ly = 10 −16  ly

Thus, 1 m= 10 −16  ly

(c)

The suitable unit conversion is,

3.0 m⋅ s −2 =3.0× 10 −3  km× 1 1  s 2 × ( 3600 s ) 2 1  h 2 =3.88× 10 4  km⋅ h −2 ≈3.9× 10 4  km⋅ h −2

Thus,

3.0 m⋅ s −2 =3.9× 10 4  km⋅ h −2 .

(d)

The suitable unit conversion is,

G=6.67× 10 −11  N⋅ m 2 ( kg ) −2 =6.67× 10 −11   kgm s 2 ⋅ m 2 ⋅ ( kg ) −2 =6.67× 10 −11   m 3 kg⋅ s 2 × 10 6   cm 3 1  m 3 × 1 kg 10 3  g =6.67× 10 −8  ( cm 3 ) s −2 g −1

Thus,

G=6.67× 10 −11  N⋅ m 2 ( kg ) −2 =6.67× 10 −8  ( cm 3 ) s −2 g −1 .