A body of moment of inertia of 3 kg - {m^2} rotating with an angular speed of 2 rad/sec has sam

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6.System of Particles and Rotational Motion

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

$1$

$ 2$

$4$

$8$

Solution

Rotational kinetic energy of the body $=\frac{1}{2} l \omega^2$ and translatory kinetic energy $=\frac{1}{2} m v^2$

According to problem $=\frac{1}{2} I \omega^2=\frac{1}{2} mv ^2 \Rightarrow \frac{1}{2} \times 3 \times(2)^2=\frac{1}{2} \times 12 \times v^2 \Rightarrow v=1 m / s$.

Standard 11

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(JEE MAIN-2020)

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medium

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

Solution

Similar Questions

Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal. Each of the rotation axes passes through the centre of the square. Then the ratio of angular speeds $\omega _1 : \omega _2 : \omega _3$ is

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