Two projectiles $A$ and $B$ are thrown with the same speed but at angles of $40^{\circ}$ and $50^{\circ}$ with the horizontal,respectively. Then:

The coordinates of a particle moving in a plane are given by $x = a \cos(pt)$ and $y = b \sin(pt)$,where $a, b (b < a)$ and $p$ are positive constants of appropriate dimensions. Then:

Two stones of masses $m$ and $2\,m$ are whirled in horizontal circles,the heavier one in a radius $\frac{r}{2}$ and the lighter one in radius $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is

If the radius of the circular path and the frequency of revolution of a particle of mass $m$ are doubled,then the change in its kinetic energy will be ($E_i$ and $E_f$ are the initial and final kinetic energies of the particle respectively). (in $E_i$)

$A$ particle of mass $M$ is moving in a circle of fixed radius $R$ in such a way that its centripetal acceleration at time $t$ is given by $n^2Rt^2$ where $n$ is a constant. The power delivered to the particle by the force acting on it,is

$A$ particle moving in the $xy$ plane experiences a velocity-dependent force $\overrightarrow{F} = k(v_y \hat{i} + v_x \hat{j})$,where $v_x$ and $v_y$ are the $x$ and $y$ components of its velocity $\overrightarrow{v}$. If $\overrightarrow{a}$ is the acceleration of the particle,then which of the following statements is true for the particle?