Question

prove 1 joule =100000000 erg

Answer 1

One joule is equal to the energy expended (or work done) in applying a force of one newton through a distance of one meter
One newton is equal to the amount of net force required to accelerate a mass of one kilogram at a rate of one metre per second squared.
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Hence
1 newton = 1 kilogram * 1 meter /second ²
1 newton = 1000 gram * 100 centi meter /second ² = 1x 10^5 (gram centi meter /second ²)
By definition (gram centi meter /second ²) is 1 dyne
Hence 1 newton = 1x 10^5 dynes
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1 joule = 1 newton*1 meter = 1x 10^5 dynes* 100 cm = 1x10^7 dyne cm
1dyne cm = 1 erg
1 joule = 1x10^7 erg
1 erg = 1x10^- 7 erg

Answer 2

1 newton = 1 kilogram * 1 meter /second ² 
1 newton = 1000 gram * 100 centi meter /second ² = 1x 10^5 (gram centi meter /second ²) 
By definition (gram centi meter /second ²) is 1 dyne 
Hence 1 newton = 1x 10^5 dynes 
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1 joule = 1 newton*1 meter = 1x 10^5 dynes* 100 cm = 1x10^7 dyne cm 
1dyne cm = 1 erg 
1 joule = 1x10^7 erg 
1 erg = 1x10^- 7 erg 

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