a solid and hollow cylinder are placed on a inclined plane and allowed to roll d

Question

a solid and hollow cylinder are placed on a inclined plane and allowed to roll downhill from the same spot. They have the same radii, but different masses. Which one rolls down quicker? Is it the same? Why? a solid and hollow cylinder are placed on a inclined plane and allowed to roll downhill from the same spot. They have the same radii, but different masses. Which one rolls down quicker? Is it the same? Why? a solid and hollow cylinder are placed on a inclined plane and allowed to roll downhill from the same spot. They have the same radii, but different masses. Which one rolls down quicker? Is it the same? Why?

Explanation / Answer

Here ,

let the mass of the hollow cycliner is m

the mass of the solid cyclinder is M

Now , for the acceleration of the hollow cyclinder ,

a(hollow cyclinder) = m * g * sin(theta)/( m + I/r^2)

a(hollow cyclinder) = m * g * sin(theta)/( m + m*r^2/r^2)

a(hollow cyclinder) = g/2

Now , for the solid cyclinder ,

a(solid cyclinder) = M * g * sin(theta)/( M + I/r^2)

a(solid cyclinder) = mM * g * sin(theta)/(M + 0.5 *M*r^2/r^2)

a(solid cyclinder) = g/1.5

Hence , as the acceleration is more for solid cyclinder ,

solid cyclinder will reach the bottom quicker.

No , the time is not same for both

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