Solveeit Logo
Login

Question

Question: A new system of units has evolved in which the values of ​\({\mu _0}\) and \({\varepsilon _0}\) are ...

A new system of units has evolved in which the values of ​μ0{\mu _0} and ε0{\varepsilon _0} are 2 and 8 respectively. Then the speed of light in this system will be (m/s)
A).0.25
B).0.5
C).0.75
D).1

Explanation

Solution

in this question, we will use the relation between the speed of light and the given medium. Further, by substituting the given values in the equation, will give us the required result. Also, we will discuss the basics of speed, for our better understanding.
Formula used:
c=1μ0ε0c = \dfrac{1}{{\sqrt {\mu {}_0{\varepsilon _0}} }}

Complete answer:
As we know, the relation between the speed of light and the given medium is given as:
c=1μ0ε0c = \dfrac{1}{{\sqrt {\mu {}_0{\varepsilon _0}} }}
Substituting the given values in the above equation, we get:
c=12×8c = \dfrac{1}{{\sqrt {2 \times 8} }}
⇒c=116=14\Rightarrow c = \dfrac{1}{{\sqrt {16} }} = \dfrac{1}{4}
∴c=0.25m/s\therefore c = 0.25m/s

Therefore, the correct option is A) i.e., the speed of light is 0.25 in meter per second.

Additional information:
As we know that the speed is a scalar quantity which means it has only magnitude not direction whereas, the average velocity is a vector quantity.
Average velocity indicates direction and can be represented as a negative number when the displacement is in the negative direction, but an average speed does not indicate direction and therefore can only be positive or zero.
Now, we already know the basic difference of speed and velocity i.e., speed is the measure of how fast an object can travel, whereas velocity tells us the direction of this speed. Speed is a scalar quantity that means it has only magnitude, whereas velocity is a vector quantity that means it has both magnitude and direction. The S.I unit of velocity is meter per second (m/sec).
A speedometer also called a speed meter is a gauge that measures and displays the instantaneous speed of a vehicle. It is mostly mounted on bikes, cars, scooters. We also know that the speedometer used to measure the speed of a vehicle and the entire vehicle indicate speed in km/h.
The speed of sound is different in different mediums. Further, the speed that is more than the speed of sound is termed differently like- supersonic, hypersonic etc

Note:
We should know that the speed of light in vacuum is given by 3×108m/s3 \times {10^8}m/s. Also, we know speed does not have any direction therefore, speed cannot be negative. We must remember that the unit of speed and velocity is the same i.e., meter per sec or m/s.