$A$ stone is projected vertically upwards with velocity $V$. Another stone of the same mass is projected at an angle of $60^{\circ}$ with the vertical with the same speed $V$. The ratio of their potential energies at the highest points of their journey is:

$A$ projectile is projected at an angle of $30^{\circ}$ from the horizontal with an initial velocity $u$. If the range of the projectile is $R$,what will be the range if the projectile is projected at an angle of $60^{\circ}$ with the same initial velocity?

$A$ smooth circular groove has a smooth vertical wall as shown in the figure. $A$ block of mass $m$ moves against the wall with a speed $v$. Which of the following curves represents the correct relation between the normal reaction $(N)$ on the block by the wall and the speed of the block $(v)$?

$A$ body moves along a circular path of radius $100 \,m$ and completes one revolution in $40 \,sec$. What is the total distance covered at the end of $2 \,min \,20 \,sec$ (in $\pi$)?

The second's hand of a watch has $6\, cm$ length. The speed of its tip and the magnitude of the difference in velocities of its tip at any two perpendicular positions will be respectively:

$A$ particle moves along a parabolic path $y = 9x^2$ in such a way that the $x$-component of velocity remains constant and has a value of $\frac{1}{3} \; m/s$. The acceleration of the particle is $....... \; m/s^2$.