Question 29: Units , Dimensions and Error Analysis

Question

A new unit ( $\alpha$ ) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes 6 min. 40 s to cover this distance?

Accepted Answer

To find the distance between two points when an object moves at a constant speed, we use formula,
Distance $=$ Speed ÃÂ Time
$\alpha$ is a new unit of length such that 1 unit $(\alpha)=$ speed of light in vacuum (c).
The speed of light c is the distance light travels per unit of time (usually meters per second).
$ 1 \alpha=c 	imes(1 	ext { second }) $
The time taken for light to travel from Venus to Earth is 6 minutes and 40 seconds.
1 minute $=60$ seconds
6 minutes $=6 	imes 60=360$ seconds
Total time $\mathrm{t}=360 \mathrm{~s}+40 \mathrm{~s}=400$ seconds
Using distance formula:
Distance $=$ Speed of light ÃÂ Time
Distance $=\mathrm{c} 	imes 400$ seconds
Since $1 \alpha$ is the distance light travels in 1 second ( $\mathrm{c} 	imes 1 \mathrm{~s}$ ), we can substitute c with our new unit,
Distance $=400 	imes(\mathrm{c} 	imes 1 \mathrm{~s})$
Distance $=400 \alpha$
Therefore, the distance between Venus and Earth is $400 \alpha$. Hence, the correct option is (B).

Answer

$200 \alpha$

Answer

$400 \alpha$

Answer

$300 \alpha$

Answer

$500 \alpha$

Units , Dimensions and Error Analysis

A new unit ( \alpha ) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of \alpha units if light takes 6 min. 40 s to cover this distance?

Choose the correct answer: