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)3s–2 g–1

Asked by Abhisek | 1 year ago |  98

1 Answer

Solution :-

(a) 1 kg m2 s–2 = ….g cm2 s–2

1 kg m2 s-2 = 1kg x 1m2 x 1s -2

We know that,

1kg = 103

1m = 100cm = 102cm

When the values are put together, we get:

1kg x 1m2 x 1s-2 = 103g x (102cm)2 x 1s-2  

= 103g x 104 cm2 x 1s-2  = 107 gcm2s-2

1kg m2 s-2 = 107 gcm2s-2

 

(b) 1 m = ….. ly

Using the formula,

Distance = speed x time

Speed of light = 3 x 108 m/s

Time = 1 yr = 365 days = 365 x 24 hr 

= 365 x 24 x 60 x 60 sec

Put these values in the formula mentioned above, we get:

One light year distance = (3 x 108 m/s) x (365 x 24 x 60 x 60) 

= 9.46×1015m

9.46 x 1015 m = 1ly

So that, 1m = 1/9.46 x 1015ly

 1.06 x 10-16ly

1 meter = 1.06 x 10-16ly

 

(c) 3.0 m s–2 = …. km h–2

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

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 = 3.88 x 104 km h-2

=> 3.0 m s-2 = 3.88 x 104 km h­-2

 

(d) G = 6.67 × 10–11 N m2 (kg)–2 = …. (cm)3s–2 g–1

G = 6.67 x 10-11 N m2 (kg)-2

We know that,

1N = 1kg m s-2

1 kg = 103 g

1m = 100cm= 102 cm

Put the values together, we get:

6.67 x 10-11 Nm2 kg-2 

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

Solve the following and cancelling out the units, we get:

6.67 x 10-11 x (1kg -1 x 1m3 x 1s-2)

Put the above values together to convert kg to g and m to cm

6.67 x 10-11 x (103g)-1 x (102 cm)3 x (1s-2)

6.67 x 10-8 cm3 s-2 -1

G = 6.67 x 10-11 Nm2(kg)-2 

= 6.67 x 10-8  (cm)3 s-2 g -1

Answered by Pragya Singh | 1 year ago

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