$A$ mass of $2 \, kg$ is whirled in a horizontal circle by means of a string at an initial speed of $5$ revolutions per minute. Keeping the radius constant,the tension in the string is doubled. The new speed is nearly ....... $rpm$.

$A$ particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a$ varies with time $t$ as $a = k^{2} r t^{2}$,where $k$ is a constant. The power delivered to the particle by the force acting on it is given as:

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:

If $T$ is the total time of flight,$h$ is the maximum height,and $R$ is the horizontal range,how are the $x$ and $y$ coordinates of projectile motion related to time $t$ and range $R$?

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?

$A$ particle is moving in the $xy$-plane and crosses the origin at time $t=0$. The equation of motion of the particle is $y=4x^2$. If the velocity of the particle is $\vec{v}=(2\hat{i}+2\hat{j}) \text{ m s}^{-1}$ and acceleration is $\vec{a}=(a\hat{j}) \text{ m s}^{-2}$, then the magnitude of $a$ is