An equilateral triangle ABC is cut from a thin solid sheet of wood… | JEE Main 2019 (11 Jan, Shift 1)

Q167JEE Main 2019 · 11 JAN · SHIFT 1Difficult

Moment of Inertia & Radius of Gyration

An equilateral triangle ABC is cut from a thin solid sheet of wood. (see figure) D, E and F are the mid- points of its sides as shown and G is the centre of the triangle. The moment of inertia of the triangle about an axis passing through G and perpendicular to the plane of the triangle is I0. If the smaller triangle DEF is removed from ABC, the moment of inertia of the remaining figure about the same axis is I. Then:

Show answer and solution

Answer: (b)

DEF has side $\frac{a}{2}$ , mass $\frac{M}{4}$ and the same centre G.
$I \propto Ma^2 \Rightarrow I_{DEF} = \frac{1}{4} \times \frac{1}{4}I_0 = \frac{I_0}{16}$
$I = I_0 - \frac{I_0}{16} = \frac{15}{16}I_0$ , so the answer is (b).

Report a mistake

More questions on Moment of Inertia & Radius of Gyration

A circular disc of radius b has a hole of radius a at its centre (see figure). If the…JEE Main 2019 (12 Apr, Shift 1)
A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment…JEE Main 2018 (16 Apr, Shift 1)
Seven identical circular planar disks, each of mass M and radius R are welded…JEE Main 2018
From a uniform circular disc of radius R and mass 9M, a small disc of radius R/3 is…JEE Main 2018
A circular hole of radius R/4 is made in a thin uniform disc having mass M and radius R…JEE Main 2017 (9 Apr, Shift 1)
Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through…JEE Main 2017 (8 Apr, Shift 1)
The moment of inertia of a uniform cylinder of length l and radius R about its…JEE Main 2017
A light rod of length l has two masses m1 and m2 attached to its two ends. The moment of…NEET 2016 (Phase 2)

Moment of Inertia & Radius of Gyration question from JEE Main 2019 (11 Jan, Shift 1)

More questions on Moment of Inertia & Radius of Gyration