The position vector of a particle \(\vec{R}\) as a function of time \(t\) is given by;
\(\overrightarrow{\mathrm{R}}=4 \sin (2 \pi \mathrm{t}) \hat{\mathrm{i}}+4 \cos (2 \pi \mathrm{t}) \hat{\mathrm{j}}\)
Where \(R\) is in meters, \(t\) is in seconds and \(\mathrm{\hat{i},\hat{j}}\) denotes unit vectors along \(\mathrm{x}\) and \(\mathrm{y}\)-directions, respectively. Which one of the following statements is wrong for the motion of the particle?
1. | acceleration is along \(-\overrightarrow{R}\). |
2. | magnitude of the acceleration vector is \(\frac{v^2}{R}\), where \(v\) is the velocity of the particle. |
3. | magnitude of the velocity of the particle is \(8\) m/s. |
4. | path of the particle is a circle of radius \(4\) m. |
A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:
1. | \(25\) m/s2 | 2. | \(36\) m/s2 |
3. | \(5\) m/s2 | 4. | \(15\) m/s2 |
A particle moves in the \((x\text-y)\) plane according to the rule \(x = a \sin (\omega t)\) and \(y = a \cos (\omega t)\). The particle follows:
1. | a circular path. |
2. | a parabolic path. |
3. | a straight line path inclined equally to x and y-axes. |
4. | an elliptical path. |