If velocity, force and time are taken as the fundamental quantities, then using dimensional analysis choose the correct dimensional formula for mass among the following. [ K is a dimensionless constant ]

Step-by-step solution

Let the quantity be Q, then, Q = f ( v , F , T ) Assuming that the function is the product of power functions of v , F and T , Q = K v x F y T z . . . ( i ) where K is a dimensionless constant of proportionality. The above equation dimensionally becomes [ Q ] = [ L T - 1 ] x [ M L T - 2 ] y [ T ] z i.e., [ Q ] = [ M y L ( x + y ) T ( - x - 2 y + z ) ] , ​Now Q = mass i.e., [ Q ] = [ M ] So Equation (ii) becomes [ M ] = [ M y L ( x + y ) T ( - x - 2 y + z ) ] its dimensional correctness requires y = 1 , x + y = 0 an