Question

A body of mass $m$ and radius $R$ rolling horizontally without slipping at a speed $v$ climbs a ramp to a height $\frac{3v^2}{4g}$. The rolling body can be:

• A. A sphere
• B. A circular ring
• C. A spherical shell
• D. A circular disc

Answer 1

Answer: (A)

A sphere

The transnational, ½mv², and the rotational, ½Iw², energy is converted into potential energy, mgh,

so from law of conserve energy,

final = initial

mgh = ½mv² + ½Iw²

= ½mv² + ½Iv²/r²

Then h is

h = (1 + I/(mr²))v² /(2g)

h = 3v²/(4g) (from data )

so

(1 + I/(mr²))v² /(2g) = 3v²/(4g)

1 + I/(mr²) = 3/2

I = ½mr²

So it is a Sphere