(a) Write the dimensional formula of the moment of inertia. (b) Four students suggest…

PHYSICS · Subjective · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

(a) Write the dimensional formula of the moment of inertia. (b) Four students suggest the following expressions for the moment of inertia of different bodies: (i)

I_1 = \dfrac{1}{3}ML

(ii)

I_2 = \dfrac{1}{12}ML^2

(iii)

I_3 = \dfrac{1}{2}MR^2

(iv)

I_4 = \dfrac{2}{5}MR^3

where

M

is mass,

L

the length of a rod, and

R

the radius of a disk or sphere as appropriate. Identify, with dimensional reasoning, which of the above expressions are dimensionally incorrect. Give clear justification for each case.

Related theory

Moment of Inertia
Dimensions of Physical Quantities
Dimensional Analysis
Dimensional formulae

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