Question

Which of the following is a unitless physical quantity?
A. Angle
B. Latent Heat
C. Specific Gravity
D. Density

Answer 1

Hint: In this question, we can determine the specific term is a unitless physical quantity based on its dimensions and units. Here, a unitless physical quantity means a physical quantity that doesn't have any unit, and also it is dimensionless.

Complete step by step solution:
Let us discuss all the options one by one. The first option is the angle. Angle is a physical quantity but it has units such as degree or radian.

Now, the second option is Latent heat. It is expressed in the form of the amount of heat.Also, its unit is joule or calorie.

Next is specific gravity. It is defined as the ratio of an element's density to the density of a reference element for the same specific volume; alternatively, we can say that it is the ratio of an element's mass to the mass of a particular element for the same given volume. As it is a ratio, it lacks a unit. Therefore, specific gravity is a unitless physical quantity.

The fourth option is density. It is the ratio of mass of an object to the volume of an object.Hence, its unit is \[{\rm{kg/}}{{\rm{m}}^3}\]or \[{\rm{g/c}}{{\rm{m}}^3}\].

Hence, the option (C) is correct.

Note:Specific gravity determines whether an element will sink or float. Many times students made a mistake in finding the formula of a given physical quantity as the unit is based on this concept. Thus, they may get difficulties in the determination of whether the given quantity is unitless or not.