Question

$Joule \times \sec$ is the unit of
A. Energy
B. Momentum
C. Angular momentum
D. Power

Answer 1

To solve this question, firstly we will consider all the given options i.e. energy, Momentum, power, and angular momentum, explain them briefly, and mention their dimensional formula. Then we will compare their dimensional formula with the dimensional formula for $Joule \times \sec$ to reach the solution.

Complete answer:
Energy – Energy refers to the ability to do work. Energy can be transferred from one object to another object which can be used to perform work. Energy exists in many forms like potential energy, kinetic energy, thermal energy, chemical energy, etc. The SI unit of energy is the ${m^2}{s^{ - 2}}kg$ . The dimensional formula of energy is $M{L^2}{T^0}$ .

Momentum – It is the product of mass and velocity of an object. Momentum is a quantity that every object in motion possesses. The SI unit for momentum is $kgs/m$ . The dimensional formula of momentum is $ML{T^{ - 1}}$ .

Angular momentum – It is the rotational equivalent of linear momentum. It is equal to the product of the radius and the linear momentum of the body in a circular motion. The SI unit for momentum is $kg{m^2}{s^{ - 1}}$ . The dimensional formula of angular momentum is $M{L^2}{T^{ - 1}}$ .
Power – It is the energy consumed per unit time. The SI unit of power is $kg{m^2}{s^{ - 2}}$ . The dimensional formula for power is $M{L^2}{T^{ - 3}}$ .

The dimensional formula for $Joule \times \sec$ is $M{L^2}{T^{ - 1}}$ .
Since the dimensional formula of angular momentum and $Joule \times \sec$ is the same
Therefore, the angular momentum is the correct answer.

So, the correct answer is “Option C”.

Note:
While solving this question, one should not confuse $Joule \times \sec$ with $joule/\sec$ as $joule/\sec$ is a unit of measurement of power and $Joule \times \sec$ is the unit of angular momentum. Aside from angular momentum $Joule \times \sec$ is also the unit of Planck’s constant, i.e. $h = 6.626176 \times {10^{ - 34}}joule - \sec$ .