What is the value of linear velocity if \(\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\)  :

The angle turned by a body undergoing circular motion depends on the time as given by the equation, $\theta ={\theta }_0+{\theta }_{1}t+{\theta }_2{t}^2$. It can be deduced that the angular acceleration of the body is? 

1. θ₁

2. θ₂

3. 2θ₁

4. 2θ₂

A car moves on a circular path such that its speed is given by v = Kt, where K =constant and t is time. Also given: radius of the circular path is r. The net acceleration of the car at time t will be:

1. $\sqrt{{\mathrm{K}}^2 + {\left(\frac{{\mathrm{K}}^2{\mathrm{t}}^2}{\mathrm{r}}\right)}^2}$

2. 2K

3. K

4. $\sqrt{{\mathrm{K}}^2 + {\mathrm{K}}^2{\mathrm{t}}^2}$

A stone tied to the end of a 1 m long string is whirled in a horizontal circle at a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?

The position vector of a particle is $\overrightarrow{\mathrm{r}}$ $=$ $\left(\mathrm{a}\right)$ $\sin$ $\mathrm{\omega t}\hat{\mathrm{i}}$ $+$ $\left(\mathrm{a}\right)$ $\cos$ $\mathrm{\omega t}\hat{\mathrm{j}}$. The velocity of the particle is:

A car is moving at a speed of 40 m/s on a circular track of radius 400 m. This speed is increasing at the rate of 3 m/s². The acceleration of the car is:

1. 4 m/s²

2. 7 m/s²

3. 5 m/s²

4. 3 m/s²

Certain neutron stars are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be:

A particle moves with constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is:

1. $2$ $\pi$ $v/T$

2. $2$ $\pi$ $r/T$

3. $2$ $\pi$ $r^2/T$

4. $2$ $\pi$ $v^2/T$