Question

Which of the following units is the unit of power?
A. Kilowatt hour
B. Watt
C. Erg
D. Calorie

Answer 1

Hint: The power applied to the object is equal to the work done by that object in one second. Thus, power is equal to work done per second. Also, the work done on an object is proportional to the Kinetic energy that is applied to it. The work done is equal to the derivative of Kinetic energy with respect to time.

Complete step by step answer:
The Kinetic energy denoted as \[T\] changes with time as:
\[\dfrac{{dT}}{{dt}} = \dfrac{d}{{dt}}\left( {\dfrac{1}{2}m{v^2}} \right) = \dfrac{1}{2}m\dfrac{d}{{dt}}({v^2}) = mv\dfrac{{dv}}{{dt}}\]
By Newton’s second law, \[m\dfrac{{dv}}{{dt}} = F\], where \[F\] is the force.
Therefore, \[\dfrac{{dT}}{{dt}} = F.v\]
The right hand side of this equation \[F.v\]is the power. The force acting on an object times the velocity of the object is the power being delivered to the object by the force. Thus, the rate of change of Kinetic energy is equal to the power expanded by the forces on it.
The unit of power is Newton-meters per second that is Joule per second. (Since, the unit of \[F.ds\]is Newton-meter). The unit Newton-meter per second is also known as Watt.
Power also equals work done per second. Since, forces are measured in Newton, and if one multiplies it by a distance in order to obtain work, then work is measured in Newton-meters or Joules. Then
\[Power = F.v = F.\dfrac{{ds}}{{dt}}\]

So, the correct answer is “Option B”.

Note:
In the solution, the mass of an object is taken to be constant by Newton’s second law. But actually in relativistic dynamics, the mass is not a constant. The mass increases for the objects that move with a very high speed. For the mass to increase it should be travelling near the speed of light and that’s too high. Thus mass is taken constant in kinematics.