Out of the following pairs which one does not have identical dimensions is Option 1) moment of inertia and moment of a force Option 2) work and torque Option 3) angular momentum and Planck’s constant Option 4) impulse and momentum

Using the concepts we learnt:

Work, Potential Energy, Kinetic Energy, Torque -

$\dpi{100} ML^{2}T^{-2}$

- wherein

$\dpi{100} N-mt/Joule$

and

Momentum-Impulse -

$\dpi{100} MLT^{-1}$

- wherein

$\dpi{100} kgms^{-1}$

and

Plank's Constant (h) -

$\dpi{100} M^{1}L^{2}T^{-1}$

- wherein

Joule-sec

Option 1)

moment of inertia and moment of a force

Moment of Inertia $\left ( I \right )= Mr^{2}$

$\therefore \; \; \; \; \left [ I \right ]= \left [ ML^{2} \right ]$

Moment of force  $rF= \left [ ML^{2} T^{-2}\right ]$

Hence moment of inertia & moment of force does not have same dimension.

Option 2)

work and torque

Work and Torque both have dimension $\left [ ML^{2}T^{-2} \right ]$

Option 3)

angular momentum and Planck’s constant

angular momentum and Planck’s constant  have dimension

$\left [ angular\: momentum \right ]= \left [ ML^{2}T^{-1} \right ]$

Also angular momentum$= \frac{h}{2\pi }$

$\therefore$ Dimension of Planck’s constant is same as angular momentum.

Option 4)

impulse and momentum

Impulse is change in momentum hence both have same dimensions.

N

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Knockout JEE Main April 2021 (Subscription)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-