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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 x 10-11 N m2 (kg)-2 = �. (cm)3 s-2 g-1

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Q(a)10^7 Q(b)1.06*10^-16 Q(c)10.8 Q(d)6.67*10^-8
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Mathematics Tutor

(a) 10^7 (b)1.06×10^-16 (C)10.8 (d)6.67×10^-8
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(a) 1 kg = 103 g1 m2 = 104 cm21 kg m2 s–2 = 1 kg × 1 m2 × 1 s–2=103 g × 104 cm2 × 1 s–2 = 107 g cm2 s–21 kg m2s–2= 107 g cm2 s–2 (b) Distance = Speed × TimeSpeed of light = 3 × 108 m/sTime = 1 year = 365 days = 365 × 24 hours... read more

(a) 1 kg = 103 g
1 m2 = 104 cm2
1 kg m2 s–2 = 1 kg × 1 m2 × 1 s–2
=103 g × 104 cm× 1 s–2 = 107 g cm2 s–2
1 kg m2s–2107 g cm2 s–2

(b) Distance = Speed × Time
Speed of light = 3 × 108 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 × 108 m/s) × (365 × 24 × 60 × 60 s) = 9.46 × 1015 m
9.46 × 1015 m = 1 ly
So that 1 m = 1/ 9.46 × 1015 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 × 104 km h–2
3.0 m s–23.88 × 104 km h–2

(d) Given,
G= 6.67 × 10–11 N m2 kg–2
We know that
1 N = 1 kg m s2
1 kg = 103 g
1 m = 100 cm = 102 cm
Putting above values, we get
6.67 × 10–11 N m2 kg–2 = 6.67 × 10–11 × (1 kg m s–2) (1 m2) (1Kg–2)
Solve and cancel out the units,

we get
⇒ 6.67 × 10–11 × (1 kg–1 × 1 m3 × 1 s–2)
Putting above values to convert kg to g and m to cm
⇒ 6.67 × 10–11 × (103 g)-1 × (102 cm)3 × (1 s–2)
⇒ 6.67 × 10–11 × 10-3 g-1 × 106 cm3 × (1 s–2)
⇒ 6.67 × 10–8 cm3 s–2 g–1
G= 6.67 × 10–11 N m2 kg–2

= 6.67 × 10–8 cm3s–2 g–1

 

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(a)10^7 (b)1.06*10^-16 (c)10.8 (d)6.67*10^-8
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Tutor

A)10^7 B)1.06*10^-16 C)10.8 D)6.67*10^-8
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Tutor

(a) 10^7 (b)1.06×10^-16 (C)10.8 (d)6.67×10^-8
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(a)10^7 (b)1.06*10^-16 Q(c)10.8 (d)6.67*10^-8
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Trainer

(a)10^7 (b)1.06×10^-16 (c)10.8 (d)6.67×10^-8
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Question (a) 10^7 Question (b)1.06×10^-16 Question (c)10.8 Question (d)6.67×10^-8
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Trainer

(a) 10^7 (b)1.06×10^-16 (C)10.8 (d)6.67×10^-8
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