If two discs have same mass and thickness but their densities are $ρ_{1}$ and $ρ_{2}$ then the ratio of their moments of inertia about central axis will be [BCECE (Mains) 2012]

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

1 : $ρ_{1}$ $ρ_{2}$

$ρ_{1}$ $ρ_{2}$ : 1

$ρ_{1}$ : $ρ_{2}$

$ρ_{2}$ : $ρ_{1}$

answer is D.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Moment of inertia of disc, $I = \frac{1}{2} M R^{2} = \frac{1}{2} M (\frac{M}{π ρ t})$

$(∵ ρ = \frac{M}{V} = \frac{M}{π R^{2} t}, ∴ R^{2} = \frac{M}{π ρ t})$

$I = \frac{1}{2} \frac{M^{2}}{π ρ t}$

$∴ I \propto \frac{1}{ρ}$ (As, M and t are constants)

$∵ \frac{I_{1}}{I_{2}} = \frac{ρ_{2}}{ρ_{1}}$

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test