Two particles of equal masses are revolving in circular paths of radii $r_1$ and $r_2$ respectively with the same speed. The ratio of their centripetal forces is

$A$ particle has an initial velocity of $(\hat{i} + \hat{j}) \, m/s$ and an acceleration of $(\hat{i} + \hat{j}) \, m/s^2$. Its speed after $10 \, s$ will be:

Two particles $A$ and $B$ are moving on two concentric circles of radii $R_1$ and $R_2$ with equal angular speed $\omega$. At $t = 0$,their positions and directions of motion are shown in the figure. The relative velocity $\overrightarrow{V_A} - \overrightarrow{V_B}$ at $t = \frac{\pi}{2\omega}$ is given by:

$A$ person moves from $A$ to $B$ on a circular path as shown in the figure. If the distance travelled by him is $60 \, m$,then the magnitude of the displacement would be $..... \, m$. (Given $\cos 135^{\circ} = -0.7$)

$A$ cyclist starts from the centre $O$ of a circular park of radius $1 \text{ km}$,reaches the edge $P$ of the park. Then,the cyclist cycles along the circumference to point $Q$ and returns to the centre along $QO$ as shown in the figure. If the round trip takes $10 \text{ minutes}$,the net displacement and average speed of the cyclist (in metre and kilometre per hour respectively) are:

Choose the correct alternative$(s)$.