Question

A solid sphere, a solid cylinder, a spherical shell, and a hoop all have the same mass and radius. Each are rolling on a horizontal surface with the same center of mass speed, and then they roll up identical inclines. Which one goes the greates distance up its incline?

a. the hoop
b. the solid sphere
c. the spherical shell
d. the cylinder
e. they all go the same distance up their inclines.

Answer 1

Answer:C) spherical shell

Explanation:

Given

A solid sphere, Solid cylinder, a spherical shell and a hoop all have same mass(m) , radius(r) and linear center of mass speed(v)

Here we need to conserve Energy i.e.

Rotational Energy + Kinetic Energy=Potential Energy

$\frac{I\omega ^2}{2}+\frac{mv^2}{2}=mgh$

where I=moment of inertia

$\omega =angular velocity$

$h=height$

$v=linear\ velocity$

I for solid sphere $=\frac{2mr^2}{5}$

I for solid cylinder $=\frac{mr^2}{2}$

I for spherical shell$=\frac{2mr^2}{3}$

I for hoop $=\frac{mr^2}{2}$

since kinetic Energy is same for all therefore moment of inertia decide which one goes higher

I for spherical shell is maximum therefore it will attain maximum height