Answer :

Answer:

Explanation:

Given

both ring and disc have mass m and radius r

Let [tex]\theta [/tex]be the inclination of plane with horizontal

[tex]f_r[/tex] be the friction force which provides torque to object

[tex]mgsin\theta -f_r=ma[/tex]

and [tex]I\alpha =f_r\times r[/tex] ---1

where I=moment of inertia

[tex]mgsin\theta -\frac{I\aplha }{r}=ma[/tex]

and we know for pure rolling a=\alpha \times r[/tex]

thus

[tex]a=\frac{gsin\theta }{1+\frac{I}{mr^2}}[/tex]

Thus Linear acceleration of ring with [tex]I=mr^2[/tex]

[tex]a=\frac{gsin\theta }{2}[/tex]

For disc [tex]I=\frac{mr^2}{2}[/tex]

[tex]a=\frac{2gsin\theta }{3}[/tex]

Angular acceleration for ring

[tex]\alpha =\frac{gsin\theta }{2r}[/tex]

For disc

[tex]\alpha =\frac{2gsin\theta }{3r}[/tex]

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