A wheel has an angular acceleration of \(3.0\) rad/s² and an initial angular speed of \(2.00\) rad/s. In a time of \(2\) s, it has rotated through an angle (in radian) of:
1. \(6\)
2. \(10\)
3. \(12\)
4. \(4\)

If a body is moving in a circular path with decreasing speed, then: (symbols have their usual meanings):

1.  $\overrightarrow{r}.\overrightarrow{\omega }$ $=$ $$ $0$

2.  $\overrightarrow{\tau }.\overrightarrow{v}$ $=$ $0$

3.  $\overrightarrow{a}.\overrightarrow{v}$ $<$ $0$

4.  All of these

Particles \(A\) and \(B\) are separated by \(10\) m, as shown in the figure. If \(A\) is at rest and \(B\) started moving with a speed of \(20\) m/s then the angular velocity of \(B\) with respect to \(A\) at that instant is:

The angular speed of the wheel of a vehicle is increased from \(360~\text{rpm}\) to \(1200~\text{rpm}\) in \(14\) seconds. Its angular acceleration will be:
1. \(2\pi ~\text{rad/s}^2\)
2. \(28\pi ~\text{rad/s}^2\)
3. \(120\pi ~\text{rad/s}^2\)
4. \(1 ~\text{rad/s}^2\)