Question

A solid cylinder and a hollow cylinder of equal mass and radius are at rest at the top of an inclined plane. They are released simultaneously and roll down the plane without slipping. Which object reaches the bottom of the incline first?

Answer 1

Solid cylinder

Step-by-step explanation:

Solid cylinder will reach first

If radius of each cylinder is r

mass is m

then,

Moment of inertia I= dm
`r^(2)`

Here d = measure as how close the mass is to the edge

Velocity of rolling cylinder is given by

v=
`\sqrt} (2gh)/(1+d)`

where,

g= 9.8 m/s2

h= height from ground

So from formula of velocity we can say that velocity will be maximum if denominator is minimum i-e if k is of small value -- or in other word if mass is away from edge i-e if mass is closer to the center !

As all the mass in hollow cylinder is near the edge so k value will be higher for it and hence it will have low velocity value. So it will reach later as compared to the solid cylinder in which mass is closer to the center and hence k is greater for solid cylinder.