An aircraft is flying at a height of $H$ above the ground at a constant speed $V$. What is the maximum angle subtended at a ground observation point by the aircraft's path after time $T$?

$A$ projectile of mass $1 \, kg$ is projected with a velocity of $\sqrt{20} \, m/s$ such that it strikes on the same level as the point of projection at a distance of $\sqrt{3} \, m$. Which of the following options are incorrect:

In a conical pendulum,the bob is rotated with different angular velocities and the tension in the string is calculated for different values of $\omega$. Which of the following is the correct graph between $T$ and $\omega$?

Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ respectively. Their speeds are such that they make complete circles in the same time $t$. The ratio of their centripetal force is

$A$ particle is moving in a uniform circular motion with angular momentum $L$. If the frequency of motion is doubled and its kinetic energy is halved,find the new value of its angular momentum.

$A$ train is moving along a straight line with a constant acceleration '$a$'. $A$ boy standing in the train throws a ball forward with a speed of $10 \ m/s$,at an angle of $60^{\circ}$ to the horizontal. The boy has to move forward by $1.15 \ m$ inside the train to catch the ball back at the initial height. The acceleration of the train,in $m/s^2$,is