Question

As observed on earth, a certain type of bacteria is known to double in number every 24 hours. Two cultures of these bacteria are prepared, each consisting initially of one bacterium. One culture is left on earth and the other placed on a rocket that travels at a speed of 0.733c relative to the earth. At a time when the earthbound culture has grown to 32 bacteria, how many bacteria are in the culture on the rocket, according to an earth-based observer?

Answer 1

Given

The speed of a rocket, v = 0.733 c

For earth,

2ⁿ = 32

2ⁿ = 2⁵

So, n = 5

By applying the time dilation formula,

t = t₀ √ [ 1 - (v/c)² ]

Here, t₀ = 5 days

t = 5 * √ [1 - (0.733c / c)² ]

t = 3.4 days

Given that the bacteria doubles every 24 hours.

So, after 3 days the number of the bactera is = 3 * 2

= 6