Rolling

Practice Questions:

Question 1: moderate

A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of 3v²/4g with respect to the initial position. The object is

1. Ring

2. Solid Sphere

3. Hollow Sphere

4. Disc

View Answer

\[ \frac{1}{2}mv^{2}+\frac{1}{2}I\omega^{2}= mgh =mg\frac{3v^{2}}{4g}= \frac{3}{4}mv^{2} \]

\[ \frac{1}{2}I\omega^{2}= \frac{1}{4}mv^{2} \]

Solving I = MR²/2 so, Object is a disc or hollow cylinder.

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Question 2: moderate

A body rolls down an inclined plane. If its kinetic energy of rotation is 40% of its kinetic energy of translation, then the body is

1. Solid cylinder

2. Solid sphere

3. Disc

4. Ring

View Answer

Given, rotational kinetic energy is 40% of total energy. so,

\[ \frac{1}{2}I\omega^{2}=\frac{40}{100}\left( \frac{1}{2}mv^{2} + \frac{1}{2}I\omega^{2} \right) \]

Solving ,

\[ I = \frac{2}{5}mR^{2} \]

Object is Solid Sphere.

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