Your hair grows at the rate of 1 mm per day. Find their growth rate in nm s⁻¹. Ans (11.57 nm s⁻¹)


Given: 

Hair Growth Rate = 1 mm per day

To find: 

Hair Growth Rate in nm s⁻¹ = ?


Solution:  

As we know

1 day = 24 hours

1 hour = 60 minutes

1 minute = 60 seconds

So, 

1 day = 24 ｘ 60 ｘ 60 s = 86,400 s ----------(1)

and

1 mm = 10⁻³ m 

In order to convert milli (10⁻³) into nano (10⁻⁹), We will multiply the R.H.S. by 10⁻⁶ ｘ 10⁶

1 mm = 10⁻³ ｘ 10⁻⁶ ｘ 10⁶ m (∴ 10⁻⁶ ｘ 10⁶ = 1)

1 mm = 10⁶ ｘ 10⁻³⁻⁶  m

1 mm = 10⁶ ｘ 10⁻⁹  m

1 mm = 10⁶ nm

or

1 mm = 1000,000 nm ------------(2)



Now as given

Hair Growth Rate = 1 mm per day 

using equations (1) and (2)

Hair Growth Rate = `\frac{1000000 nm}{86,400 s}`

by simplifying we get

Hair Growth Rate = 11.57 nm s⁻¹ -----------Ans


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