A solid disk and a solid sphere each of mass M and radius R are released at the same time from the top of an inclined plane. which object will reach the bottom first? Justify your answer. Show complete derivation.

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A solid disk and a solid sphere each of mass M and radius R are released at the same time from the top of an inclined plane. which object will reach the bottom first? Justify your answer. Show complete derivation.

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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dont go away i am going to solve this problem..
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for normal reaction, N= mgcosa

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for motion down the inclined plane, F= mg sina - f ............(1)
since friction prevents slipping and frictional force is causing rotation with angular acceleration @ thus torque, T = f*R = I*@
f= I*@/R = I*a/R^2
m*a=mgsina - I*a/R^2
if frictionless [ you did not specify], then same but if they are rolling, the cylinder will be slower as has a greater I [as it is more "spread out" about the rotating axis] to prove that, personally i'd use energy conservation for this rather than forces as its a lot less fiddly
a= gsina - I*a/R^2
now if u put the value of moment of inertia for sphere and disc, u get the the linear acc downward...
thank you guys :D
do u know what is moment of inertia for sphere and disc....
greater the linear acc. more faster the object reaches the ground faster.....
got it?
yes :)
yes we've already had an experiment about this one. thank you again :)
good job @lall
thanks! @IrishBoy123
their moment of inertia can be calculated mathematically.....

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