Question

Four solid rigid balls each of mass m and radius
rare fixed on a rigid-ring of radius 2r and mass
2m. The system is whirled about 'O' as shown.
The radius of gyration of the system is :
2m
(0 ha
cerves​

Answer 1

Answer:

hope this help you

Answer 2

The radius of gyration is $r\sqrt{\dfrac{128}{30}}$

Explanation:

Given that,

Mass of each four solid balls = m

Radius = r

Radius of ring = 2r

Mass of ring = 2m

We need to calculate the moment of inertia

Using formula of moment of inertia

I=moment of inertia of the ring+ moment of inertia of the ball

$I=m_{r}r_{r}^2+4(\dfrac{2}{5}mr^2+mr^2)$

Put the value into the formula

$I= 2m(2r)^2+4(\dfrac{2}{5}mr^2+m(2r)^2)$

$I=8mr^2+\dfrac{8}{5}mr^2+16mr^2$

$I=\dfrac{128}{5}mr^2$

We need to calculate the radius of gyration

Using formula of radius of gyration

$K=\sqrt{\dfrac{I}{m}}$

Put the value into the formula

$K=\sqrt{\dfrac{\dfrac{128}{5}mr^2}{(4+2)m}}$

$K=r\sqrt{\dfrac{128}{30}}$

Hence, The radius of gyration is $r\sqrt{\dfrac{128}{30}}$

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Topic : radius of gyration

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