Question

Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):

 

the number of strands of hair on your head

Answer 1

Area of the head surface carrying hair = A

With the help of a screw gauge, the diameter and hence, the radius of a hair can be determined. Let it be r.

∴Area of one hair = πr²

Number of strands of hair ${\displaystyle \approx \frac{\text{Total surface area}}{\text{Area of one hair}\pi }=\frac{A}{r^2}}$

Answer 2

Let us assume that the man is not partially bald. Let us further assume that the hair on the head are uniformly distributed. We can estimate the area of the head. The thickness of a hair can be measured by using a screw gauge. The number of hair on the head is clearly the ratio of the area of head to the cross-sectional area of a hair.

Assume that the human head is a circle of radius 0.08 m i.e., 8 cm. Let us further assume that the thickness of a human air is 5 x 10^-5m.

Number of hair on the head =Area of the head/Area of cross – section of a hair

=π (0.08)2/π(5 x 10^-5)=64 x 10-4/25 x 10^-10=2.56 x 10⁶

The number of hair on the human head is of the order of one million.