Question

A physical quantity is given by \(A =\dfrac{mv}{qB}\), where m is the mass, v is the speed, q is the charge, and B is the magnetic field. The dimension of A will be-

1. [L]
2. [M]
3. [T]
4. Dimensionless

Answer 1

Correct Answer - Option 1 : [L]

CONCEPT:

• Dimensional formula: It is a compound expression showing which of the fundamental quantities are involved and how are they involved in making that physical quantity.

Quantity	Dimensional formula
Force (F)	[MLT-2]
velocity (v)	[LT-1]
Inertia (I)	[M1L2T3]
Magnetic Field (B)	[M1 L0 T-2 A-1].
Charge (Q)	[AT]
Spring constant (K)	[ML0T-2]
Length	[L]
Work (W)	[ML2T-2]
Any constant (C)	No dimension

CALCULATION:

Given quantity \(A =\dfrac{mv}{qB}\)

Take dimensions of both sides

\([A] =\dfrac{[m][v]}{[q][B]}\)

\([X] =\dfrac{[M][LT^{-1}]}{[AT][MT^{-2}A^{-1}]}\)

\([X] =[L]\)

• So the correct answer is option 1.