A solid square plate is spun around different | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The rotational kinetic energy of a body is given by $K = \frac{1}{2} I \omega^2$,where $I$ is the moment of inertia and $\omega$ is the angular sp

Vedclass · Accepted Answer

Through one corner normal to the plate

Vedclass · Answer

(D) The rotational kinetic energy of a body is given by $K = \frac{1}{2} I \omega^2$,where $I$ is the moment of inertia and $\omega$ is the angular speed.Since $\omega$ is constant for all cases,the kinetic energy $K$ is directly proportional to the moment of inertia $I$ $(K \propto I)$.Therefore,the kinetic energy will be largest for the axis about which the moment of inertia $I$ is maximum.For a square plate of side $a$ and mass $M$:$1$. Axis through the centre,normal to the plate: $I_1 = \frac{Ma^2}{6}$$2$. Axis along a diagonal: $I_2 = \frac{Ma^2}{12}$$3$. Axis along an edge: $I_3 = \frac{Ma^2}{3}$$4$. Axis through a corner,normal to the plate: Using the perpendicular axis theorem,$I_4 = I_{cm} + M(r^2) = \frac{Ma^2}{6} + M(\frac{a}{\sqrt{2}})^2 = \frac{Ma^2}{6} + \frac{Ma^2}{2} = \frac{4Ma^2}{6} = \frac{2Ma^2}{3}$.Comparing the values,$I_4$ is the largest. Thus,the kinetic energy is largest when the plate is rotated about an axis through one corner normal to the plate.

$A$ solid square plate is spun around different axes with the same angular speed. In which of the following choices of axis of rotation will the kinetic energy of the plate be the largest?

Similar Questions

The moment of inertia of a uniform rectangular plate about an axis passing through its center and parallel to its length $(l)$ is ($b =$ width of the rectangular plate):

For the adjoining diagram,the incorrect relation between $I_{1}, I_{2}$ and $I_{3}$ is ($I$ = moment of inertia).

Four spheres each of diameter $2a$ and mass $M$ are placed with their centres on the four corners of a square of side $b$. Then the moment of inertia of the system about an axis along one of the sides of the square is

Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a Cartesian coordinate system with one end of all the rods at the origin. The moment of inertia of the system of the rods about the $z$-axis is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module