1kg m^2 s^-2 is equal to? a)10^2gm cm^2 s^-2 b) 10^5gm cm^2 s^-2. c) 10^7gm cm^2 s^-2. D)10^9gm cm^2 s^-2

1 Answer
Hriman
Aug 5, 2018

C.

Explanation:

Use dimensional analysis (the whole point of it is to cancel units out to get the desired units):

#(1 cancel(kg)m^2)/(s^2)xx(1000 g)/(1cancel(kg))=10^3g *m^2 *s^-2#

Now to convert #m^2# to #cm^2#, you have to be careful since the units are squared, we know that in #1m# there is #100 cm#

#(1m)/(100cm)#, however if we want to go from #m^2# to #cm^2#, we simply square the values

#(1m)^2/(100cm)^2= (1m^2)/(10000 cm^2)#

Now we resume our calculation:
#(10^3g *cancel(m^2))/(s^2)xx(10^4cm^2)/(cancel(m^2))=10^7g *cm^2 *s^-2#

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