Question

Dimensional formula of velocity of sound is
A. ${M^0}L{T^{ - 2}}$
B. $L{T^0}$
C. ${M^0}L{T^{ - 1}}$
D. ${M^0}{L^{ - 1}}{T^{ - 1}}$

Answer 1

To answer this question, we know what dimensional formula is and after that we must know what the formula for the velocity of sound is. Dimensions of the physical quantity are the power to which the base quantities are raised to represent that quantity.

Formula used:
$v = \dfrac{d}{t}$
Where, $v$ is the velocity, $d$ is the distance and $t$ is time.

Complete step by step answer:
We know that there will be the same dimensional formula for linear velocity as well as velocity of sound because they both are the same physical quantity i.e., velocity.We can see here the dimensions of $d$ is length and is directly proportional so we can write $L$ and $t$ i.e., time and is inversely proportional so we can write ${T^{ - 1}}$.And there is no mass so we can write ${M^0}$. So, the complete dimensional formula for velocity is $[{M^0}L{T^{ - 1}}]$ .

Hence, the correct option is C.

Additional information: A dimensional equation is an equation that relates fundamental units and derived units in terms of dimensions. In mechanics, the length, mass, time, temperature, and electric current are taken as three base dimensions, and meter, kilogram, second, ampere, kelvin, mole, and candela are the fundamental units. The dimensional formula of individual quantities is used to establish a relationship between them in any dimensional equation.

Note: Dimensions are denoted with square brackets. In mechanics, mass, length, and time are the basic quantities and the units used for the measurement of these quantities are known as fundamental units. Dimensional equation is that equation obtained by equating the physical quantity with its dimensional formula. For example, the dimensional formula for mass is given as $[M{L^0}{T^0}]$ and the dimensional formula for length is $[{M^0}L{T^0}]$.