Consider a badminton racket with length scales as shown in the… | JEE Main 2021 (26 Aug, Shift 1)

Q140JEE Main 2021 · 26 AUG · SHIFT 1Medium

Moment of Inertia & Radius of Gyration

Consider a badminton racket with length scales as shown in the figure.

If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at $\frac{r}{2}$ distance from the end A of the handle will be ................ Mr2.

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

Show answer and solution

Answer: 52

Handle: length $6r$ , centre $3r$ from A, so $2.5r$ from axis: $\frac{M(6r)^2}{12} + M(2.5r)^2 = 9.25Mr^2$
Ring: radius $r$ , centre $7r$ from A, so $6.5r$ from axis; axis is parallel to a diameter.
Ring: $\frac{Mr^2}{2} + M(6.5r)^2 = 42.75Mr^2$
Total $= 52Mr^2$ , so the answer is $52$ .

Report a mistake

More questions on Moment of Inertia & Radius of Gyration

Three point masses, each of mass m are placed at the corners of an equilateral triangle…MHT CET 2020 (19 Oct, Shift 2)
A thin uniform rod has mass M and length L The moment of inertia about an axis…MHT CET 2020 (16 Oct, Shift 2)
The radius of gyration of a uniform rod of length l, about an axis passing through a…JEE Main 2020 (7 Jan, Shift 1)
A massless equilateral triangle EFG of side ‘a’ (As shown in figure) has three particles…JEE Main 2020 (3 Sep, Shift 2)
Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing…JEE Main 2020 (3 Sep, Shift 1)
The ratio of radii of gyration of a ring to a disc (both circular) of same radii and…MHT CET 2020 (16 Oct, Shift 2)
For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia…JEE Main 2020 (4 Sep, Shift 2)
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)

Moment of Inertia & Radius of Gyration question from JEE Main 2021 (26 Aug, Shift 1)

More questions on Moment of Inertia & Radius of Gyration