Question

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

Answer 1

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`