$A$ 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 $A$ moves along the line $y=30 \ m$ with a constant velocity $v$ parallel to the $x$-axis. At the moment particle $A$ passes the $y$-axis,a particle $B$ starts from the origin with zero initial speed and a constant acceleration $a=0.40 \ m/s^2$. The angle between $a$ and the $y$-axis is $60^{\circ}$. If the particles $A$ and $B$ collide after some time,then the value of $|v|$ will be (in $m/s$)

$A$ particle moves in space according to the equation $\vec{r} = (\sin t \hat{i} + \cos t \hat{j} + t \hat{k}) \text{ m}$. Find the time $t$ when the position vector and acceleration vector are perpendicular to each other.

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is $R_0 = 10 \, m$. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $v = 20 \, m/s$,on a horizontal surface? $(g = 10 \, m/s^2)$

For a given initial velocity,a projectile is fired at angles of $30^\circ$ and $60^\circ$. Find the ratio of their maximum heights.

If a body of mass $2 \,kg$ moving with an initial velocity of $4 \,m \,s^{-1}$ is subjected to a force of $3 \,N$ for a time of $2 \,s$ normal to the direction of its initial velocity, then the resultant velocity of the body is