Answer:Sphere
Explanation:
Given
sphere and cylinder are released are released at same time to roll without slipping
While rolling acceleration of an object is given by
[tex]a=\dfrac{g\sin \theta }{1+\frac{I}{mr^2}}[/tex]
where [tex]\theta [/tex]=inclination of Plane
I=moment of Inertia of body
m=mass of object
r=radius of object
Moment of inertia of cylinder is
[tex]I=\frac{mr^2}{2}[/tex]
Moment of inertia of sphere is
[tex]I=\frac{2}{5}mr^2[/tex]
Suppose they are released from a height h so time taken to reach bottom is given by
[tex]t=\sqrt{\dfrac{2h}{a}}[/tex]
thus [tex]t\propto \dfrac{1}{\sqrt{a}}[/tex]
acceleration of cylinder is less as compared to sphere because its MOI is high
thus time taken by cylinder is more compared to sphere
Therefore sphere will reach first at bottom
