JEE Main202311 Apr 2023Evening ShiftPhysicsUnits and DimensionsActual
If force ( F ) , velocity ( V ) and time ( T ) are considered as fundamental physical quantity, then dimensional formula of density will be :
Options
- A  F   V 4   T - 6
- BF   V - 4   T - 2
- CF 2   V - 2   T 6
- DF   V - 2   T 2
Correct answer
B. F   V - 4   T - 2
Step-by-step solution
The dimensional formula of force is F = M L T - 2 The dimensional formula of velocity is V = L T - 1 The formula for density is Density = M L 3 = M L - 3 Comparing the density dimensions with the assumed fundamental quantities in the question, M L - 3 = F x V y T z ⇒ M L - 3 = M L T - 2 x L T - 1 y [ T ] z ⇒ M L - 3 = M x L ( x + y ) T - 2 x - y + z Comparing the exponents, x = 1       . . . ( i ) x + y = - 3       . . . ( i i ) - 2 x - y + z = 0       . . .