find the value of 60 joule per minute on a system which has 10 cm,100gm, and 1 minute as fundamental units.
216*10^6gcm^@min^-3
To find the value of 60 joule per minute on a system with 10 cm, 100 gm, and 1 minute as fundamental units, we need to convert the units of joule, which is the SI unit of energy, into the given fundamental units.
First, let's look at the units of joule:
1 joule = 1 kg * m^2/s^2
Now, let's break down the given fundamental units and their respective dimensions:
- 10 cm: This represents a length, and since 1 cm = 0.01 m, we can say that 10 cm = 0.1 m. Therefore, the dimension of length is represented by [L] = m.
- 100 gm: This represents mass, and since 1 gm = 0.001 kg, we can say that 100 gm = 0.1 kg. Therefore, the dimension of mass is represented by [M] = kg.
- 1 minute: This represents time, and since 1 minute = 60 seconds, we can say that 1 minute = 60 s. Therefore, the dimension of time is represented by [T] = s.
Now, let's break down the dimensions of joule and express it in terms of the given fundamental units:
1 joule = (1 kg * m^2/s^2) = (1 kg * (1 m)^2 / (60 s)^2) = (1 kg * 1 m^2 / 3600 s^2)
Now, we can relate this expression to the given value of 60 joule per minute:
60 joule per minute = (60 * 1 kg * 1 m^2 / 3600 s^2) per minute
As we see, the "per minute" term cancels out:
60 joule per minute = (60 * 1 kg * 1 m^2 / 3600 s^2) = (60 / 3600) kg * m^2 / s^2
Therefore, 60 joule per minute in the given system is equal to (60 / 3600) kg * m^2 / s^2, which can be simplified further if needed.