### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2008

The dimension of magnetic field in M, L, T and C (coulomb) is given as
A
MLT-1C-1
B
MT2C-2
C
MT-1C-1
D
MT-2C-1

## Explanation

We know that,
Lorentz force $\left| {\overrightarrow F } \right| = \left| {q\overrightarrow v \times \overrightarrow B } \right|$

$\therefore [B]$ = ${[F] \over {[q][v]}}$ = ${[{ML{T^{ - 2}}]} \over {[C] \times [L{T^{ - 1}}]}}$ = [$M{T^{ - 1}}{C^{ - 1}}$]
2

### AIEEE 2005

Out of the following pair, which one does NOT have identical dimensions is
A
angular momentum and Planck's constant
B
impulse and momentum
C
moment of inertia and moment of a force
D
work and torque

## Explanation

Moment of inertia, I = Mr2

$\therefore$ [I] = [ML2]

Moment of force, $\overrightarrow \tau = \overrightarrow r \times \overrightarrow F$

$\therefore$ $[\overrightarrow \tau ]$ = $[L][ML{T^{ - 2}}]$ = $[ML^{ 2}{T^{ - 2}}]$
3

### AIEEE 2004

Which one of the following represents the correct dimensions of the coefficient of viscosity?
A
ML-1T-1
B
MLT-1
C
ML-1T-2
D
ML-2T-2

## Explanation

From stokes law, Viscous force F = $6\pi \eta rv$

$\Rightarrow \eta = {F \over {6\pi rv}}$

$\therefore$ $[\eta] = {[{ML{T^{ - 2}}]} \over {[L][L{T^{ - 1}}]}}$

$\Rightarrow [\eta] = [M{L^{ - 1}}{T^{ - 1}}]$
4

### AIEEE 2003

The physical quantities not having same dimensions are
A
torque and work
B
momentum and Planck's constant
C
stress and Young's modulus
D
speed and ${\left( {{\mu _0}{\varepsilon _0}} \right)^{ - 1/2}}$

## Explanation

Momentum = mv = [${M{L}{T^{ - 1}}}$]

Planck's constant, h = ${E \over v}$ = ${[{M{L^2}{T^{ - 2}]}} \over {[{T^{ - 1}}]}}$ = $[{M{L^2}{T^{ - 1}}}]$

So Momentum and Planck's constant do not have same dimensions.