Question

Consider two bodies A and B with respective angular speeds 2 rad/s and 4 rad/s. If they have same mass and same rotational kinetic energy then the ratio of radius of gyration is

Answer 1

Answer:

2:3

Explanation:

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Answer 2

Given:

Angular speed of body A = 2 rad/s

Angular speed of body B = 4 rad/s

To find:

The ratio of radius of gyration of the two bodies.

Solution:

We know that radius of gyration

$k = \sqrt{ \frac{i}{m} }$

where m is the mass of the body and I is the moment of inertia.

We are given that they have same rotational kinetic energy.

And kinetic energy is given by

$\frac{1}{2} i {w}^{2}$

where w is the angular velocity.

So,

$\frac{1}{2} i1 {w1}^{2} = \frac{1}{2} i2 {w}^{2}$

$\frac{1}{2} i1 ({2}^{2}) = \frac{1}{2}i2 ({4}^{2} )$

$i1 = 4i2$

Ratio of radius of gyration will be:

$\frac{k1}{k2} = \sqrt{ \frac{i1}{i2} }$

$\frac{k1}{k2} = \sqrt{ \frac{4i2}{i2} }$

k1/ k2 = 2/1

Therefore the ratio of radius of gyration is 2:1.