The moment of inertia of a solid disc rotating along its diameter is… | JEE Main 2025 (28 Jan, Shift 1)

Q48JEE Main 2025 · 28 JAN · SHIFT 1Medium

Moment of Inertia & Radius of Gyration

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is $n$ times higher than the moment of inertia of the given ring. Here, $n =$ ________ Consider all the bodies have equal masses.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 4

Equal masses, so radii differ. Disc about diameter $\frac{1}{4}MR_d^2$ , ring about diameter $\frac{1}{2}MR_r^2$ .
$\frac{1}{4}R_d^2 = 2.5 \times \frac{1}{2}R_r^2 \Rightarrow R_d^2 = 5R_r^2$
Sphere (radius $R_d$ ): $I_s = \frac{2}{5}MR_d^2 = 2MR_r^2$ .
$n = \frac{2MR_r^2}{\frac{1}{2}MR_r^2} = 4$

Report a mistake

More questions on Moment of Inertia & Radius of Gyration

Moment of inertia of a solid sphere about its diameter is 'I'. It is then casted into 27…MHT CET 2025 (26 Apr, Shift 1)
Moment of inertia of the rod about an axis passing through the centre and perpendicular…MHT CET 2025 (26 Apr, Shift 1)
A thin metal wire of length ' L ' and mass ' M ' is bent to form semicircular ring as…MHT CET 2025 (22 Apr, Shift 2)
Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing…MHT CET 2025 (21 Apr, Shift 2)
Two circular loops P and Q of radii ' r ' and ' nr ' are made respectively from a uniform…MHT CET 2025 (21 Apr, Shift 1)
Two discs A and B of same material and thickness have radii R and 3R respectively. Their…MHT CET 2025 (20 Apr, Shift 1)
A rod of linear mass density 'λ' and length 'L' is bent to form a ring of radius 'R'…JEE Main 2025 (8 Apr, Shift 2)
Moment of inertia of a rod of mass ' M ' and length ' L ' about an axis passing through…JEE Main 2025 (2 Apr, Shift 1)

Moment of Inertia & Radius of Gyration question from JEE Main 2025 (28 Jan, Shift 1)

More questions on Moment of Inertia & Radius of Gyration