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

$A$ ball of mass $m$ is thrown vertically upwards. Another ball of mass $2m$ is thrown at an angle $\theta$ with the vertical. Both of them stay in air for the same period of time. The heights attained by the two balls are in the ratio of

$A$ particle moves from the point $(2.0\hat i + 4.0\hat j) \, m$ at $t = 0$ with an initial velocity $(5.0\hat i + 4.0\hat j) \, m/s$. It is acted upon by a constant force which produces a constant acceleration $(4.0\hat i + 4.0\hat j) \, m/s^2$. What is the distance of the particle from the origin at time $t = 2 \, s$?

Four persons $P, Q, R$ and $S$ are initially at the four corners of a square of side $d$. Each person now moves with a constant speed $v$ in such a way that $P$ always moves directly towards $Q$,$Q$ towards $R$,$R$ towards $S$,and $S$ towards $P$. The four persons will meet after time:

$A$ particle starts from the origin at $t=0$ with a velocity $5 \hat{i} \text{ m/s}$ and moves in the $x-y$ plane under the action of a force which produces a constant acceleration of $(3 \hat{i} + 2 \hat{j}) \text{ m/s}^2$. If the $x$-coordinate of the particle at that instant is $84 \text{ m}$,then the speed of the particle at this time is $\sqrt{\alpha} \text{ m/s}$. The value of $\alpha$ is . . . . . . .

Balls $A$ and $B$ are thrown from two points lying on the same horizontal plane separated by a distance of $120\,m$. Which of the following statement$(s)$ is/are correct?