Velocity Analysis of Pure Rolling

Q. A circular disk of a radius R rolls without slipping at a velocity V. The magnitude of the velocity at point P (see figure) is:

1. $\sqrt{3}V$
2. $\sqrt{3}\frac{V}{2}$
3. $\frac{V}{2}$
4. $\frac{2V}{\sqrt{3}}$

Q. A circular object of radius r rolls without slipping on a horizontal level floor with the center having velocity V. The velocity at the point of contact between the object and the floor is

1. Zero
2. V in the direction of motion
3. V opposite to the direction of motion
4. V vertically upward from the floor

Q. In figure, the velocities are in ground frame and the cylinder is performing pure rolling on the plank, velocity of point 'A' would be

1. $2V_C$
2. $2V_C+V_P$
3. $2V_C-V_P$
4. $2(V_C-V_P)$

Q. The cylinder shown below rolls without slipping. Toward which of the following points is the acceleration of the point is the acceleration of the point of contact A on the cylinder directed?

1. The mass centre
2. The geometric centre
3. The point P as marked
4. None of the above

Q. The centre B of a wheel rolling on a plane surface moves with a speed $V_0$. The speed of point A, B and C are respectively

1. $V_0,V_0,2V_0$
2. $V_0,V_0,0$
3. $\sqrt{2}{V}_0,V_0,2V_0$
4. $\sqrt{2}{V}_0,V_0,V_0$