Instantaneous Centre of Rotation

Q. A rod of length 1 m is sliding in a corner as shown in figure. At an instant when the rod makes an angle of 60 degrees with the horizontal plane, the velocity of point A on the rod is $1\frac{m}{s}$. The angular velocity of the rod at the instant is

1. $2\frac{rad}{s}$
2. $1.5\frac{rad}{s}$
3. $0.5\frac{rad}{s}$
4. $0.75\frac{rad}{s}$

Q. A circular disk of radius r is confined to roll without slipping at P and Q as shown in the figure.

If the plates have velocities as shown, the magnitude of the angular velocity of the disk is

1. $\frac{3v}{2r}$
2. $\frac{v}{2r}$
3. $\frac{v}{r}$
4. $\frac{2v}{3r}$

Q. Instantaneous centre of a body rolling without sliding on a stationary curved surface lies.

1. At the point of contact
2. On the common normal at the point of contact
3. On the common tangent at the point of contact
4. At the centre of curvature of the stationary surface

Q.

As shown in figure, person A is standing at the centre of a rotating platform facing person B who is riding a bicycle, heading East. The relevant speeds and distances are shown in the given figure, a bicycle, heading East. At the instant under consideration, what is the apparent velocity of B as seen by A?

1. $3\frac{m}{s}$ heading east

2. $3\frac{m}{s}$ heading west

3. $8\frac{m}{s}$ heading east

4. $13\frac{m}{s}$ heading east

Q. A roller of diameter 200 mm rolls without slipping between two horizontal strips moving in oppsosite directions as shown in figure. The instantaneous center of rotation of roller lies on the line PQ at a distance from Q equal to

1. 0
2. 80 mm
3. 100 mm
4. 200 mm