Question

The dimensional formula of Areal velocity is:
(A) ${M^0}{L^{ - 2}}{T^{ - 1}}$
(B) ${M^0}{L^{ - 2}}{T^1}$
(C) ${M^0}{L^2}{T^{ - 1}}$
(D) ${M^0}{L^2}{T^1}$

Answer 1

Hint: Areal velocity is a measure of the velocity of one celestial body orbiting another, equal to the field that the vector joining the two bodies sweeps out per unit of time. In terms of simple quantities, the dimensional formula is an expression for the unit of a physical quantity. Mass (M), length (L), and time (T) are the fundamental quantities. In terms of M, L, and T powers, a dimensional formula is expressed.

Complete step by step answer: Areal velocity is a measure of the velocity of one celestial body in orbit about another, equal to the area swept out per unit time by the vector joining the two bodies.
Thus, Areal velocity = Area covered/ Time taken
Or, $Areal\,\,velocity = \frac{A}{T} = A{T^{ - 1}}$……(i)
Now, the dimensional formula of Area covered (A) = [${M^0}{L^2}{T^0}$]
Dimensional formula of time taken (T) = [${M^0}{L^0}{T^1}$]
Substituting the dimensional formula values of area and time in equation (i), we get,
$A{T^{ - 1}} = \dfrac{{[{M^0}{L^2}{T^0}]}}{{[{M^0}{L^0}{T^1}]}} = [{M^0}{L^2}{T^{ - 1}}]$
Thus, the dimensional formula of areal velocity is $[{M^0}{L^2}T{}^{ - 1}]$
Hence, option (C) is the correct option.

Note: In this question you are asked to find the dimensional formula of Areal velocity. Here, we must remember the concept of the dimensional formula. In this solution initially, we write down the formula of areal velocity and then we note down the dimensional formula of area and time. Using these dimensional formulas we easily found the dimensional formula of areal velocity which is a measure of the velocity of one celestial body orbiting another, equal to the field that the vector joining the two bodies sweeps out per unit of time.