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JEE Mains Previous Years Questions with Solutions

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1

AIEEE 2003

MCQ (Single Correct Answer)
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.
2

AIEEE 2003

MCQ (Single Correct Answer)
Dimensions of $${1 \over {{\mu _0}{\varepsilon _0}}}$$, where symbols have their usual meaning, are
A
[ L-1T ]
B
[ L-2T2 ]
C
[ L2T-2 ]
D
[ LT-1 ]

Explanation

The velocity of light in vacuum is

c = $${1 \over {\sqrt {{\mu _0}{\varepsilon _0}} }}$$;

$$\therefore[{1 \over {{\mu _0}{\varepsilon _0}}}]$$ = [c2] = [L2T-2]

$$\therefore$$ Dimension of $${1 \over {{\mu _0}{\varepsilon _0}}}$$ = [L2T-2]
3

AIEEE 2002

MCQ (Single Correct Answer)
Identify the pair whose dimensions are equal
A
torque and work
B
stress and energy
C
force and stress
D
force and work

Explanation

Work (W) = $$\overrightarrow F .\overrightarrow s $$ = Fs cos$$\theta$$

= [MLT-2][L] = [ML2T-2];

Torque ($$\overrightarrow \tau) = \overrightarrow r \times \overrightarrow F $$ $$ \Rightarrow \tau = rF\sin \theta $$

= [L] [MLT-2] = [ML2T-2]

So dimension of torque and work are same.

Questions Asked from Units & Measurements

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