A solid square plate is spun around different axes with same angular speed. In which of following ch

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6.System of Particles and Rotational Motion

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

Through the centre, normal to the plate

Along one of the diagonals of the plate

Along one of the edges of the plate

Through one corner normal to the plate

(KVPY-2009)

Solution

(d)

Kinetic energy of a rotating body is

$K=\frac{1}{2} I \omega^2$

where, $I=$ moment of inertia of a body.

For square plate, moment of inertia is largest along an axis perpendicular to plane of plate and through its one of corner. As mass distribution is now farthest from axis of rotation.

So, kinetic energy of plate is largest in option $(d)$.

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

Solution

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A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The radio $\frac{{{h_{sph}}}}{{{h_{cyl}}}}$ is given by

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A thin hollow cylinder open at both ends:

$(i)$ Slides without rotating

$(ii)$ Rolls without slipping, with the same speed