Units and Measurement

Question

Find the unit of power in a system of unit, in which unit of mass is 20kg, unit of force is 10N and unit of energy is 5J.

Solution

The dimensional formula of power in terms of mass, force and energy.
Let the dimensional formula of power in terms of mass, force and energy is [M^aF^bE^c].
i.e. Power, P = [M^aF^bE^c]
Equating both sides of above equation dimensionally,

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets straight M to the power of 1 straight L squared straight T to the power of negative 3 end exponent close square brackets space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets straight M to the power of 1 straight L to the power of 0 straight T to the power of 0 close square brackets to the power of straight a open square brackets straight M to the power of 1 straight L to the power of 1 straight T to the power of negative 2 end exponent close square brackets to the power of straight b open square brackets straight M to the power of 1 straight L squared straight T to the power of negative 2 end exponent close square brackets to the power of straight c rightwards double arrow open square brackets straight M to the power of 1 straight L squared straight T to the power of negative 3 end exponent close square brackets equals open square brackets straight M to the power of straight a plus straight b plus straight c end exponent straight L to the power of 0 plus straight b plus 2 straight c end exponent straight T to the power of negative 2 straight b minus 2 straight c end exponent close square brackets

Comparing the dimensions of M, L and T on both sides, we get
a + b+ c = 1 ...(1)
b + 2c = 2 ...(2)
-2b -2c = -3 ...(3)
Solving (1), (2) and (3), we get

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Substituting the value of units of m, F and E in equation (4), we get

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In new system, the unit of power is 5W.

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Units And Measurement

Find the unit of power in a system of unit, in which unit of mass is 20kg, unit of force is 10N and unit of energy is 5J.

Some More Questions From Units and Measurement Chapter

Define physical quantity.

Give four examples of physical quantities.

Define unit.

What are the two main required characteristics of a unit?

Can we use same units for different physical quantities?

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

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