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

English

Gujarati

Hindi

6.System of Particles and Rotational Motion

medium

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 $(d)$.

Standard 11

Physics

Three particles are situated on a light and rigid rod along $Y$axis as shown in the figure. If the system is rotating with an angular velocity of $2\,rad/\sec $about $X$axis, then the total kinetic energy of the system is …… $J$

medium

A hollow sphere of mass $m$ filled with a non-viscous liquid of same mass $m$ is released on a slope inclined at angle $q$ with the horizontal. The friction between the sphere and the slope is sufficient to prevent sliding and frictional forces between the inner surface of the sphere and the liquid is negligible. After descending a certain height ratio of translational and rotational kinetic energies is found to be $x:y$, find the numerical value of expression $(x+y)_{min}.$

hard

A body of moment of inertia of $3\ kg-m^2$ rotating with an angular velocity of $2\ rad/sec$ has the same kinetic energy as a mass of $12\ kg$ moving with a velocity of ………. $m/s$

medium

$A$ thin rod $AB$ is sliding between two fixed right angled surfaces. At some instant its angular velocity is $ \omega $. If $I_x$ represent moment of inertia of the rod about an axis perpendicular to the plane and passing through the point $X$ ($A, B, C$ or $D$), the kinetic energy of the rod is

hard

$A$ sphere of mass $M$ and radius $R$ is attached by a light rod of length $l$ to $a$ point $P$. The sphere rolls without slipping on a circular track as shown. It is released from the horizontal position. the angular momentum of the system about $P$ when the rod becomes vertical is :

normal

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

Similar Questions

Three particles are situated on a light and rigid rod along $Y$axis as shown in the figure. If the system is rotating with an angular velocity of $2\,rad/\sec $about $X$axis, then the total kinetic energy of the system is …… $J$

A body of moment of inertia of $3\ kg-m^2$ rotating with an angular velocity of $2\ rad/sec$ has the same kinetic energy as a mass of $12\ kg$ moving with a velocity of ………. $m/s$

$A$ thin rod $AB$ is sliding between two fixed right angled surfaces. At some instant its angular velocity is $ \omega $. If $I_x$ represent moment of inertia of the rod about an axis perpendicular to the plane and passing through the point $X$ ($A, B, C$ or $D$), the kinetic energy of the rod is

$A$ sphere of mass $M$ and radius $R$ is attached by a light rod of length $l$ to $a$ point $P$. The sphere rolls without slipping on a circular track as shown. It is released from the horizontal position. the angular momentum of the system about $P$ when the rod becomes vertical is :

Start a Free Trial Now