Student Login

Home›Chapters›Rotational Motion PYQs›Moment of Inertia & Radius of Gyration›Question 147

JEE Main 2020 (4 Sep, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2020 (4 Sep, Shift 2)

Q147JEE Main 2020 · 4 SEP · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is:

Show answer and solution

Answer: (b)

Through centre O: $I_O = \frac{M}{12}(a^2 + b^2)$ .
O' is a corner, at distance $\frac{1}{2}\sqrt{a^2 + b^2}$ from O: $I_{O'} = \frac{M}{12}(a^2+b^2) + \frac{M}{4}(a^2+b^2) = \frac{M}{3}(a^2+b^2)$ .
$\frac{I_O}{I_{O'}} = \frac{1/12}{1/3} = \frac{1}{4}$
So the answer is (b) $\frac{1}{4}$ .

Report a mistake

More questions on Moment of Inertia & Radius of Gyration

Two circular loop A and B of radii R and NR respectively are made from a uniform wire…MHT CET 2020 (19 Oct, Shift 2)
Consider two uniform discs of the same thickness and different radii R1 = R and R2 = α R…JEE Main 2020 (4 Sep, Shift 2)
Three solid spheres each of mass m and diameter d are stuck together such that the lines…JEE Main 2020 (9 Jan, Shift 1)
A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane…JEE Main 2020 (5 Sep, Shift 2)
Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M…JEE Main 2020 (6 Sep, Shift 1)
ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid points of AB…JEE Main 2020 (4 Sep, Shift 1)
The linear mass density of a thin rod AB of length L varies from A to B as λ(x) =…JEE Main 2020 (6 Sep, Shift 2)
Mass per unit area of a circular disc of radius a depends on the distance r from its…JEE Main 2020 (7 Jan, Shift 2)