Question

convert 5 newton into dyne using dimensional analysis

Answer 1

as we know the dimensional formula of force:- [M1L1T-2]

so the powers we get a=1,b=1 and c=-2 
as we know that force is in M.K.S system so M1=1kg, L1=1m, T1=1s

and M2=1g, L2=1cm , T2=1s

n1=5 N and n2=?

n2=n1[M1/M2]a [L1/L2]b [T1/T2]c    (putting a,b and c powers)

n2=5[1kg/1g]1 [1m/1cm]1 [1s/1s]-2

n2=5[1000g/1g] [100cm/1cm]    (converted in g,cm, and time will be cancel out)

n2=5x1000x100 

n2=500000 dynes....

hope it is clear......

Answer 2

Concept introduction:

Dyne is force when mass measured in grams, time in seconds and length in centimeter.

Explanation:

Given that, $5N$ of force.

We have to find, value of given force in dyne.

According to the question,

we know the dimensional formula of force:- $[M^{1} L^{1} T^{-2} ]$

so the powers we get $a=1,b=1, c=-2$

as we know that force is in M.K.S system so $M1=1kg, L1=1m, T1=1s$

and $M2=1g, L2=1cm , T2=1s$

$n1=5 N$ and $n2=?$

$n2=n1[M1/M2]a [L1/L2]b [T1/T2]c$  (putting a, b and c powers)

$n2=5[1kg/1g]^1 [1m/1cm]^1 [1s/1s]^-^2$

$n2=5[1000g/1g] [100cm/1cm]$   (converted in g, cm, and time will be cancel out)

$n2=5x1000x100$

$n2=500000 dynes$

Final Answer:

Value of given force in dyne is: $500000 Dynes$.

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