Rolling

Question 1:

A disc is rolling (without slipping) on a horizontal surface C is its centre and Q and P are two points equidistant from C. Let v_P, v_Q and v_C be the magnitude of velocities of points P, Q and C respectively, then

1. \[ V_{Q}> V_{C}> V_{P} \]

2. \[ V_{Q}< V_{C}< V_{P} \]

3. \[ V_{Q}= V_{P }, V_{C}= \frac{1}{2} V_{P} \]

4. \[ V_{Q}< V_{C}> V_{P} \]

View Answer

During pure rolling the point on ground acts as instantaneous axis of rotation. Distance from the point of contact with ground determines speed of point. so,

\[ V_{Q}> V_{C}> V_{P} \]

Question 2:

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.

Question 3:

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.