The hour hand of a clock is $6\,cm$ long. The magnitude of the displacement of the tip of the hour hand between $1:00\,PM$ and $5:00\,PM$ is:

$A$ particle of mass $m$ moves with constant speed $v$ on a circular path of radius $r$ as shown in the figure. The average force on it during its motion from $A$ to $B$ is

$A$ wheel of radius $R$ is trapped in a mud pit and spinning. As the wheel is spinning,it splashes mud blobs with initial speed $u$ from various points on its circumference. The maximum height from the centre of the wheel,to which a mud blob can reach is

$A$ particle of mass $m$ is projected with velocity $v$ making an angle of $45^\circ$ with the horizontal. When the particle lands on the level ground,the magnitude of the change in its momentum will be

Two particles move on a circular path (one just inside and the other just outside) with angular velocities $\omega$ and $5\omega$ starting from the same point. Then

$A$ particle moves from the point $(2.0\hat i + 4.0\hat j) \, m$ at $t = 0$ with an initial velocity $(5.0\hat i + 4.0\hat j) \, m/s$. It is acted upon by a constant force which produces a constant acceleration $(4.0\hat i + 4.0\hat j) \, m/s^2$. What is the distance of the particle from the origin at time $t = 2 \, s$?