Answer:
a) solid sphere. Assuming no air resistance
Explanation:
If they all have the same mass and radius, the torque will be the same, but since their inertia is different, the angular acceleration will be different.
[tex]\tau = I*\alpha[/tex] => [tex]\alpha =\frac{\tau}{I}[/tex]
So, the one with the biggest acceleration will be the one with the smallest inertia.
The inertia for each object, in ascending order are:
Solid Sphere = [tex]\frac{2}{5} *m*R^2=0.4*m*R^2[/tex]
Solid Cylinder= [tex]\frac{1}{2} *m*R^2=0.5*m*R^2[/tex]
Sphere Shell= [tex]\frac{2}{3} *m*R^2=0.67*m*R^2[/tex]
Cylindrical Shell= [tex]m*R^2=m*R^2[/tex]
As you can see, the solid sphere has the smallest inertia, and therefore, will have the greatest acceleration. (All of this assuming there is no air resistance)
