Question

A solid sphere, spherical shell, solid cylinder and a cylindricalshell all have the same mass m and radius R. Ifthey are all released from rest at the same elevation and rollwithout slipping, which reaches the bottom of an inclined planefirst

a) solidsphere
b) sphericalshell
c) solidcylinder
d) cylindricalshell
e) all take the sametime

Answer 1

a) solid sphere. Assuming no air resistance

Step-by-step 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.

`\tau = I*\alpha` =>
`\alpha =(\tau)/(I)`

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 =
`(2)/(5) *m*R^2=0.4*m*R^2`

Solid Cylinder=
`(1)/(2) *m*R^2=0.5*m*R^2`

Sphere Shell=
`(2)/(3) *m*R^2=0.67*m*R^2`

Cylindrical Shell=
`m*R^2=m*R^2`

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)