Velocity: Bottom Most Point

Q.

Consider a wheel purely rolling on a rough horizontal surface with constant velocity v. Radius of the wheel is R and C is the center of wheel. M is top-most point, P is bottom-most point and N is in level with C at any time. Match the columns for this instant of time.

1. (p-w, x); (q-x, y); (r-w, x); (s-w, x)

2. (p-w) (q-x, y) (r-w, y) (s-w, z)

3. (p-y, z) (q-y, z) (r-w, x) (s-y)

4. (p(w, x) (q-w, x) (r-w, x) (s-w, x)

Q. A car whose radius of tire is 30 cm is travelling at a speed of 54 km/h on a straight road. Find angular speed of tire(assume there is no slipping between tire & road).

1. 20 rad/sec
2. 180 rad/sec
3. 50 rad/sec
4. 10 rad/sec

Q. Two plates 1 and 2 move with velocities $-v$ and $2v$ respectively. If the sphere does not slide relative to the plates, assuming the masses of each body as $m$, find the kinetic energy of the system (plate+sphere).

1. $\frac{125}{40}m{v}^2$
2. $\frac{123}{40}m{v}^2$
3. $\frac{23}{90}m{v}^2$
4. $\frac{23}{40}m{v}^2$