Question

If the unit of power is \[{1_{}}Kilo - Watt\] the length is \[100m\] and time \[1s\], then the unit of mass will be?
(A) \[10kg\]
(B) \[{10^{ - 1}}kg\]
(C) \[100kg\]
(D) \[{10^{ - 2}}kg\]

Answer 1

Hint We know the formulas that are used to define power. In this case, assume that the mechanical power is equal to the electric power. Equate the formulas and find the mass.

Complete Step By Step Solution
Let us understand the given terms. Electrical power P is given as \[{1_{}}Kilo - Watt\]. Length of a mechanical operation or string is said to be \[100m\] and the time period is \[1s\]. We are required to find the unit of the mass and the calculated value.
Let us first understand the definitions of power. Electric power is defined as the rate of work or energy that is transferred by an electric circuit. It can also be said as a product of source voltage and the current flowing in a circuit.
Mechanical power is defined as the amount of energy transferred or work done an object per unit time. Dimensionally, both the Si units are Watts. In mechanical power, the output is calculated in terms of Newton- Meter/Seconds, which is dimensionally equal to 1 watt.
Given in a mechanical system, the length of an object , due to work done is 100m, which means that the object has moved 100m, from its original state due to work. Therefore, it can also be equal to displacement of the object.
Applying power formula.
\[P = \dfrac{W}{t} = \dfrac{{F \times s}}{t}\]
We know that power is 1 kilowatt , that is equal to \[1000W\]
\[1000 = \dfrac{{F \times 100}}{1}\]
\[F = 10N\]
We know, force is the product of mass and acceleration,
\[F = m \times a\]
Mass is unknown and assuming a as \[1m/{s^2}\], we get
\[m = 10kg\]

Hence, Option (a) is the right answer for the given question.

Note
Electric power is given as the product of current flowing inside a given circuit and total voltage difference across a circuit.
Mathematically, \[P = V \times I\]